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I refer to the dreaded Yu-Gi-Oh, of course, thus violating my own thread title. Way to go, me. I'm making this post for the purpose of linking to friends if necessary, though I wish for the community to see my reasoning and possibly critique it. This is intended as my complete argument for why I prefer the game Magic: the Gathering to Yu-Gi-Oh.

First, I will disclose my credibility or lack thereof, depending on your view:

I do not consider myself a Magic Pro at all. My history with the game started in Scourge, ended with Betrayers of Kamigawa, and then I got back into the game right about when Mirrodin Beseiged was released, and I continue playing to this day. My preferred formats are Commander and Modern.

Likewise, I am something of a novice to Yu-Gi-Oh, but I have played it over the past few months with the intent of being able to share hobbies with friends, and so I could make educated comparisons between the two games.

I will compare and contrast the following categories:

Deck Construction
Competitive Play
Ease of Play/Understanding
Flavor
Game Balance
Fun Factor
Art
Management by Host Company

Deck Construction:

Comparing: The Deck-and-Sideboard format is the primary similarity. Each game also features a limit on the number of specific card copies, 4 for MTG and typically 3 for YGO.

Contrasting: The similarities end there. You all know how MTG deckbuilding works, so I will skip explaining that. YGO features an "Extra Deck" of up to 15 cards that can be tapped into by the effects of other cards. The Extra Deck is not drawn from at the start of turns, it can be thought of as a circumstantial "toolbox" pool of cards that can be accessed when appropriate. The deck size is minimum 40, maximum 60. No Battle of Wits for YGO. However, YGO also does not have to accomodate for lands or ever worry about mana restrictions.

My Analysis:  MTG has a more rigid deck construction theme, barring 100-card formats like Commander. YGO has the advantage of only having a 40-card minimum, and I will concede that smaller decks are more reliable and theoretically cheaper. I will concede that advantage to YGO, though it is worth remembering that too much deck reliability can be a bad thing, contributing to repetitive gameplay. We'll return to this later when I address Game Balance.

Competitive Play:

Comparing: General consensus I've found between players of both games is that competitive players are a frequent source of unfun jerk behavior. Virtually everyone who has played in a tournament has encountered someone unpleasant. Competition can bring out the worst in people, so this is hardly surprising.

Contrasting: YGO has 2 formats: One where cards are restricted or banned completely, one where anything goes. MTG has Standard, Commander, Modern, Legacy, Vintage, and various other less-popular formats like Extended, Pauper, Prismatic, etc. YGO is arguably easier to get into from a competitive aspect as one's cards will never "expire" from a format unless outright banned.

Aside: A typical YGO player only knows of MTG's Standard and sometimes Vintage formats, only having heard hearsay. Attempts to educate them of Modern, Commander, or the like typically results in "LA LA LA I AM NOT LISTENING I WILL ONLY HOLD ONTO MY FALSE PRECONCEPTIONS" in some form or another. My opinion of such people's intelligence is low. People are entitled to their opinions, but for goodness' sake why can't they be educated opinions?

Contrasting, resumed: YGO has deck archetypes much like how MTG does. However, the archetypes are spoon-fed to YGO players. Imagine deck archetypes being organized by creature type rather than deck function, except that the cards are all named in a unifying way that qualifies them as a tribe rather than their creature type (Elves vs. Goblins Duel Decks would literally all have the name Elf or Goblin in every card by YGO standards). 

For example, take Mono-Black Control as an archetype. It will hold cards from a diversity of sets. Thoughtseize from Lorwyn, Abyssal Persecutor from Worldwake, Damnation from Planar Chaos, maybe a Core Set Smallpox instead of the original. This requires strategic thinking and card consideration from across Magic's history.

Now look at YGO. Decks are basically printed in one go. You get Hieratic Dragons all being printed at once. Earthbound Immortals (YGO's Eldrazi) all at once, Inzektors (more on these later!), Steelswarm, Gishki, Numbers, HERO (details later), Six Samurai, Wind-Up, Toon World, and the list goes on for literally pages and pages.

This is NOT universal, however, and there are a satisfying amount of decks (Such as decks centered around probably the only YGO cards every MTG player will know: Exodia, Dark Magician, Blue-Eyes) that violate this rule. 

My Analysis: YGO's archetypes are more varied, but good lord are they spoonfed to the players.  This becomes a recurring issue, "MTG for Dummies" being an insult of choice, though I feel the games are distinct from another enough that that's not true. However, it is hard to deny that YGO has a much easier entry barrier than MTG when it comes to competitive play due to the simplified formats.

Ease of Play/Understanding: 

Comparing: Uh. Given this is a relative category to each game, there is no comparison.

Contrasting: YGO is simpler, hands down. There's no stack, there's no priority, there's no comprehensive rule PDF that dwarfs the US Tax Code. I'm sorry, fellow fans of MTG, but I'd be making a completely biased, untrue statement if I called MTG the simpler game. However, that simplicity is also a flaw in YGO. Let me explain the issues of not having lands and mana as a balancing system, for example.

In Magic, the mana system functions to restrict the options a deck has. A given Red deck isn't going to be tutoring cards or countering spells (barring wacky standouts like Gamble) due to mana balancing. Mana is the supreme checks-and-balances system in MTG. Blue is supposed to have trouble with aggressive creature strategies, for example. Delver and his ilk aside. When you try to have more effects and options from across the color pie, you sacrifice deck consistency for utility. This also helpfully keeps stupid things from happening unless a deck is custom-tailored to enable those stupid things, and most stupid things are engineered to have counters in other colors or even colorless cards (such as Relic of Progenitus).

In YGO, there is no "color checks and balances" system. So what can be used to create game balance? The Tribute Summon part of the game worked out at first, before mechanics like Synchro Summon and XYZ Overlay came about. Well, the answer is rarity. People who play MTG complain about the Mythic Rarity regularly.

We have it way, way better than YGO players.

MTG Rarity levels: Basic Land, Common, Uncommon, Rare, Mythic Rare, Timeshifted.

YGO Rarity levels: Oh my god. Common is split into Normal Rare, Short Print, Supershort Print, and Holofoil Rare. Rare, the next level, is split into Super Rare, Ultra Rare, Ultimate Rare, Ghost Rare, and Holographic Rare. Then you get Secret Rare: Prismatic Secret Rare, Ultra Secret Rare, and Secret Ultra Rare (I'm not joking). Next comes Parallel Rare: Normal Parallel Rare, Super Parallel Rare, Ultra Parallel Rare, and Starfoil Rare. Finally, Gold Rares: Gold Ultra Rare, Gold Secret Rare, and Ghost/Gold Rare. This doesn't even count alternative rarity printings that vary from product to product.

My local card shop owner told me that you can easily tell the money value of a given YGO card by how shiny the card is, as each rarity level makes more and more of the card foil. (And yes, you can determine which booster packs have foils in them because of this, said owner even demonstrated this to me.)

This is a trainwreck. "Lotus Cobra is a terrible card because its a cheap Mythic Rare with incredible utility and fits into so many decks!" True, but count your blessings!  At least it can't be played in literally every deck if someone wanted, unlike YGO, and at least it isn't Super Holofoil Tapdance Quasi-Interstellar Wallet Molestation Rare.

Yes, it's "simpler" game balance than Mana, but holy profanities I can't post, man!

Analysis: If you want an easy game to learn, choose YGO. If you want a game with relative balance, choose MTG. 

Flavor:

Comparison: Little in the way of similarities here.

Contrast: Planeswalker duels and world-spanning storylines versus, uh...



That.

Analysis: I'm pretty sure even some YGO fans think the CHILDREN'S CARD GAMES thing is idiotic. The exception to this came up when I discussed this point with a Dungeon Master who ran a roleplay community, however. It is much easier and less intrusive to storytelling to design an ordinary person who plays a card game than it is to invent a Planeswalker. Additionally, Abridged Series parodies basically exist at all because of how stupid the premise to YGO is, and I'll call that an acceptable trade.

Game Balance:

Contrasting:  I got ahead of myself earlier with YGO's rarity trainwreck situation. I'm going to tell you a pair of stories.

Story 1:

There once was a deck called Inzektors.  It was an aggressive deck that led to incredible board swarm positions, and could pull out spot-removal effects by sacrificing Inzektor monsters to other Inzektor monsters, thus clearing the way for your Inzektor swarm to make alpha strikes every turn. The sheer speed of the deck hinged on the fact that each Inzektor typically benefitted from the amount of Inzektors in play. Due to the Synchro Summon mechanic, the more Inzektors you had out, the more Inzektors you could easily play. Inzektors dominated tournaments easily.

Story 2:

There once was a deck called Ravager Affinity. It was an aggressive deck that led to incredible board swarm positions, and could pull out spot-removal effects by sacrificing artifacts to Shrapnel Blast, thus clearing the way for your artifact swarm to make alpha strikes every turn. The sheer speed of the deck hinged on the fact that each artifact typically benefitted from the amount of artifacts in play. Due to the Affinity mechanic, the more artifacts you had out, the more artifacts you could easily play. Ravager Affinity dominated tournaments easily.

And now we reach the branching path. Wizards took one look at what Ravager Affinity did and banned half the cards in the deck. Konami looked at Inzektors and said "This is fun gameplay, let's make all our deck archetypes like this from now on!"

My friend who plays competitive YGO is basically disgusted by the game's current state. It's literally a race between the players to see who can swarm the board fastest and use monsters to cheat out more monsters while destroying enemy monsters, leading to incredibly samey gameplay. 

This isn't like Caw-Blade being all over the place in competitive play at its peak. This would be like if Innistrad printed a "Rockforge Shaman" Goblin and a slew of amazing equipment along with Jace, Master of Card Advantage. And then Dark Ascension printed a "Treeforge Druid" Elf and some sort of gothic horror Living Weapon card set, along with Jace the Card Bouncer. And then Avacyn Restored saw "Waveforge Wizard" the Spirit, various equipment that tutored for other equipment ala Sunforger, and Jace, Jace of Jace. And so on. 

Analysis: Advantage MtG. I see players complain about balance issues, or power creep, or whatever, but it is nowhere near as degenerate as YGO.  

Fun Factor:

Comparison: Again, this is a contrast-only category.

Despite all the above, casual YGO is quite enjoyable, and very easy to just pick-up-and-play. YGO is a creature-centric game, creatures power out creatures which power out creatures. YGO has very meager Control cards outside of full-blown board lockdowns or sweepers. This means that it's aggro versus aggro, and that's an easy strategy to build around in YGO. Once you leave casual play, however, the concerns of acquiring a Stardust Transcendant XYZ Rainbow Dragon playset come into effect. 

Analysis: Candle vs. Stick of Dynamite. MTG is a "slow burn" game that takes a while to learn the nuances of, and gameplay is less fast-paced and swingy compared to YGO. YGO is an "explosion" of fun, easy to get into at first, but once you get past the initial enthusiasm and start reaching for serious play, the fun is all gone. You can see why people who only play a little of each game will lean towards YGO more, as YGO structurally supports new players while MTG is relentlessly complex. Learning Curve variances lead to different amounts of payoff in the long term.

Art:

 ...Yeah. Anime artstyle is a simplistic thing. I appreciate visual simplicity, but it leads to monotony, as everything winds up looking the same.

Look at the guy's face on Molting Skin . You can tell that he's Japanese, he's from Kamigawa after all. Now look at basically any other set's humans, and you'll see Caucasians. You can clearly distinguish the western-influenced character designs from the eastern. Molting Skin in particular made me appreciate MTG art more than any other card. MTG's art is detailed, there's work put into it, and cards are only monotonous in appearance when that's the entire point (such as White Phyrexian cards from New Phyrexia). 

Analysis: No contest. Japanophiles will prefer their anime, but everyone else will side with the non-cartoony art styles. I mean, here's some contrasting images featuring similar subjects:

 Molten Destruction vs. Volcanic Awakening

Red Nova Dragon vs. Moonveil Dragon

 Lightning Vortex vs. Warstorm Surge

Cosmic Horror Gangi'el vs. Emrakul, the Aeons Torn

And so on.

Management by Host Company:

...How long have I been typing this essay/rant, good lord!? The last category, finally! Contrasting only.

Contrasting:  

Wizards of the Coast have been naughty in the past. Mythic Rarity leaves a bad taste in peoples' mouths generally, and some cards they've outright said should never have been printed, like Skullclamp. The banlists are updated a few times per year, and no emergency bans have taken place in a very, very long time. Playtesting of products is an important job that is taken seriously.

You saw the rarity fiasco Konami runs. Konami's banlist functions more like a "List of Things We Don't Pay Attention To." Let me show you one particular favorite, I have a theory that Konami doesn't actually playtest their cards at all.

Meet Yata-Garasu. The last line of text, for those too lazy to click the link reads, "When this card inflicts Battle Damage to your opponent, they skip their next Draw Phase".

You have got to be kidding me. Needless to say, the thing was banned swiftly, but for a while all it took was one poke from Yata-Garasu after a board/hand wipe to completely lock the opposing player out of being able to do anything for the rest of the game. Yeah. The YGO Forbidden Card list reads like a note I'd write to myself before going to the grocery store. If not outright forbidden, a card is casually put on the Restricted list, limiting the number of copies one can put in their deck. Band-Aid solutions are good, right?

In short, Konami handles their game very poorly, between absurd rarities being the only game-balancer, pathetic cards that clearly never saw playtest, and the general sense I get is that YGO is popular in spite of anything Konami has done rather than because of their management.

Final Conclusion: 

Play MTG if you want an actual fulfilling game experience over the long-term, play YGO if you're just doofing around now and then with buddies.

Let the arguing begin. 

As someone whose friends played mainly Yugioh and playing it heavily myself let me comment on a few subjects:

Inzektors:
They were a tier 1 deck for a little bit, but they were the weakest of the top 3 decks of Wind-Ups, Inzektors, and Dino-Rabbit. Inzektors are used to defeat grinding decks that do not go off in 1 turn.

Ease of play:
Yugioh is easier to access, but at higher levels of play you have to deal with spell speeds, properly special summoning, and missing the timing which are very complicated and nit picky rules that are slightly difficult to understand, furthermore there is priority (which has been altered recently) and the stack does exist.

-There are 3 levels of spell speeds: A Spell Speed 1 card or effect can only be activated/cast when the active player has priority (casting a creature or activating an ability). A Spell Speed 2 card or effect can be activated at anytime while there is not a Spell Speed 3 card on the stack and the active player has pass priority or used a Spell Speed 1 or 2 card or effect. Spell Speed 3 cards and effects are typically reactive and require something to happen (such as an effect activating or a monster being summoned) and once they activate only another Spell Speed 3 effect can activate.

-Properly special summoning a creature allows you to fetch it from the graveyard with a reanimation effect. There are some effects that special summon a creature from the Extra Deck, but when it hits the graveyard it won't be able to be ressurected by an effect unless it is returned to the Extra deck by some ability and is special summoned correctly.

-Some reactive effects can only be used when something happens, and that condition must be the last thing that happened in the game. There is a card called Petin the Dark Clown, and when it is destroyed you can special summon a copy of it from your deck. If you sacrifice Petin the Dark Clown as the cost for an ability to activate you cannot special summon a clown from your deck as the last thing to happen was the effect of whatever you sacrificed Petin for; therefore you missed the timing on the card and cannot activate its ability.

-Counters: Hoo-boy there are counters is Yugioh, although not every deck can play them. Heralds aims to get a Herald of Perfection onto the field and protecting it so that you can negate enemy cards until you draw into one of the "Boss Creatures" and beatdown like a typical W/U deck. Dino-Rabbits tries to quickly get out cards that will slow the game down so that they can slowly beatdown the opponent with 1 or 2 slightly large creatures. Antimeta uses cards that distrupts your opponent and beats down with a few medium sized creatures. Wind-Ups uses pure attrition and hand-discard to set up game ending turns and massive card advantage. Modolches uses medium sized creatures that grant pure card advantage and backrow support to grind out the enemy. Inzektors are relatively small, but can deal with decks that can't kill in one turn while setting up to create an army of relatively large monsters. Furthermore, most decks can put in Solemn Warning (negates a creature being summoned at the cost of a lot of life points) or a Solemn Judgment (negates a single card from being played at the cost of half of your life points) which must be used strategically to mess up your oppoents plans.

Competitive Play and Deck Themes:
Yes there are themes already laid out, but one aspect you forgot to mention was that so many cards were printed so that there are many different variations of the same theme and some tier 1 decks aren't actually made off of a premade theme.

-Different Decks made with a single theme: There are an infinite number of HERO decks out there, ranging from Bubble Beatdown which aims for a super fast kill by quickly getting out a Rank 4 XYZ to smack down  your opponent quickly (think Red Deck Wins using rituals to create mana to summon a Flame Titan on turn 2 at the cost of huge card disadvantage) to the typical Toolbox Hero that uses fusions to get out a variety of relatively large monsters to deal with different situations.

-Decks that do not have a spoon fed theme: Dino-Rabbits uses several cards that are not from a theme to create a control-tempo style of deck.

Flavor:
If you look  at a lot of the cards some do tell stories across the cards.

Management:
Konami uses the banlist to keep degenerate decks from dominating and to knock down some tier 1 decks. Recently restrictions and bans hit the top 3 decks (Inzektors, Dino-Rabbit, and Wind-Ups) taking away some of their degenerate behavior and making them slightly less consistant. The Yatagaratsu lock was only used for 1 format (which rotates twice a year) and Konami does not ban/limit cards during the middle of a format. Let it be known that Yatagarastu was when the game was really, really young and before R&D knew what they were doing. 

Well Deus sets up a lockdown, but if Bubble Beatdown fails to kill with it's attack or it is disrupted then the Bubble Beatdown player has to awkwardly scoop.