Now, I have only played characters from 3rd ed (and 3.5) and 4th, though have seen some material from earlier editions and have found information brought up on these boards very interesting, so here are my thoughts:
Artificer: One person in my play group is all over the artificer, and he LOVES the way the 4e one is presented. However, he is very big on magic item creation, and has definitely noted the difficulties the game has had with it.
Assassin: The shadowy assassin is really cool, and it was neat that 4e attached it to a different power source (Shadow), though the 3.x prestige class did feel kind of right conceptually (that a character of whatever class would become an assassin after time). I will also admit to being in the group that thinks that assassin could be done quite well as a rogue package of some sort lol.
Avenger: Obviously only around in 4e. It was an interesting class (always amusing stealthing around with a great weapon), though I think it was most interesting for its mechanical innovation (was a striker that gained what is now Advantage on attacks vs special target instead of bonus damage). As a concept, never found it terribly special; if it got folded into Paladin as the striker/dps style I wouldn't shed any tears hahaha.
Barbarian: Kind of torn here. 3.x managed to get the feel of the simple, raging barbarian really well. However, I lauded 4e in that its barbarian was finally truly different from a fighter (to which it felt waaaay too similar in 3rd), though I can understand not everyone digging the totemic channeling thing. I think keeping the primal source but having a sort of simple, inner rage character and an exotic, totem/channeling based rager would be really cool.
Bard: Being able to dabble in everything is really interesting, but can make it really hard to be a useful character. In 3rd especially, our groups had trouble with bards. 4e did a spectacular job by really propelling the bard's role forward (it was always supposed to be a 'leader' class), though I don't know how many people took advantage of the multiclass freedom it had.
Cleric: I am the token cleric in my playgroup, and I LOVE the 4e cleric. It allowed you to really make a more spellcasty cleric or a melee cleric and both were perfectly good. As melee, I was still behind the fighter in hitting, but was really close so I wasn't useless swinging a weapon (some of that bonus coming from taking superior/exotic proficiency which closes the gap), and even my basic melee attacks helped the group. I'll say that again, as 5th totally doesn't have anything like it: my at-will abilities let me buff or help my party. That was revolutionary! Melee clerics need love
. That being said, 2e kits looked VERY interesting, and I am loving the deity system in 5e right now (though I would argue for allowing a clothy spellcaster or an armored warrior of ANY god lol). Special shout-out to Divine Power form 3.x though: it was broken when you got to cast it half a dozen times a day (poor overshadowed fighter D
, but once, maybe twice it was really, really cool.
Druid: This gets tough. 3rd really encompassed all that people come to think of when you mention 'druids' in fantasy now. However, it did everything a bit too much (the whole CoDzilla scene). One nice step 4e did was separating Primal from Divine, and that added great flavor. The base 4e druid was really neat, and got the shapeshifting and nature casting down pretty well, but a) lacked the healing, leader aspect (until essentials), and b) could have used more differentiating between druid that specialized elsewhere and one that really shapeshifted (different forms doing different things for the specialist, like a tank-y large animal form vs a dps-y one). I think if you made a druid that had base, although very limited, access to wildshape, nature spells, and heal/buff spells, and then made the druid specialize into one of those 3 to get the really useful effect, that could be cool.
Fighter: 4e fighter was a really nice piece of design, and it was great to see fighters get some abilities and some actual mechanics to help fulfill a guardian-like role. That being said, a) it was lacking a striker path (until essentials) and I can appreciate the beauty of the simple tree structure of the 3rd ed fighter. It was very pick up and play with a massive amount of customization. Someone mentioned earlier here the fighter's transformation in the Star Wars Saga Edition Soldier class, and I totally agree: it kept much of the simple elegance of the 3rd ed fighter, but added the talent trees to allow for soldier-only cuztomization and for special abilities if you wanted. Honestly, a fighter with a guardian, slayer, and warlord class feature and talent tree would be AMAZING! (sorry warlord for stitching you on to fighter!)
Monk: I think I like the feel of the 3.x monk better than the 4e monk, even if the 4e monk did a nice job of being its own thing. The 4e monk was cool, and had really innovative designs, but making it entirely psoinic was kind of weird and kind of made it lose some of its old flavor. (though I can appreciate others' opinions here about the troubles portraying the monk class over the years and the difficult task Wizards has).
Paladin: The first think I said when I saw the 4e paladin was "omg evil paladins!" I almost totally agree with an earlier poster about how cool the black guard was in 3rd, but I was always irritated that it was only a prestige class - that good guys got a divine champion from lvl 1 but bad guys didn't; we even made a reversed paladin to make an evil one once. So for 4e, the ability to make a villain right out of the gate was really great (beyond getting useful defendery mechanics). That being said, some people want a more leadery paladin and others a more strikery one, so I support a class feature where you get a choice of 1 of 3 things that will take you down the corresponding path. I am also cool with paladins are good, except in the rare case where they are evil (and those beings of pure darkness are to be feared, so when the party runs into an armored bad guy who busts out divine magic they're like O__O).
Psion: This is a rough one. Psion in 3rd was really neat, but was a giant mess, especially trying to tie in all the stats. It also suffered a LOT from "just a wizard but different" syndrome. 4e REALLY limited the purview of psions, but gave them a very unique mechanic that truly differentiated them from the arcane casters, which was great.
Ranger: Ranger's another tough one to tackle conceptually. 3rd might have had it with the animal companion and limited magic really making it different from a fighter. The 4e one was really neat, and felt kind of different, but how much of that was just role and range.... (otoh, I know people that like the non-magical ranger too, so....).
Rogue: In all truth, the rogue didn't change all that much from 3rd to 4th. They both had more skills, and special skills, than the others, and both did crazy damage with combat advantage/flanking. The 4e one tightened up the math though, which was really nice. And gave it some neat skill based abilities (which I will admit 3rd got with the Complete Scoundrel and skill tricks, but were just tighter in 4e).
Shaman: I don't think it was around in 3rd. Honestly found this one really strange and had wonky mechanics; I would have been totally cool with a healy druid lol. That being said, some people on the boards swear by shamans, so if there are people that like 'em, all the power to them.
Sorcerer: 4e definitely over the 3rd ed version. In 3.x, it was waaaaaay too similar to a wizard. In 4e, the combination of different role (though restricted roles is a point of contention and striker wizard does make sense), interesting bloodline mechanics (the chaos sorceror was HILARIOUS and fun) and a different spell list (courtesy of every class having its own powers) made it feel truly its own thing compared to wizard. This does become an admittedly difficult scenario to keep now. A friend and I were even considering whether or not there should be some schools of magic open to the innate caster but not the learned one, and vice-versa, so really push the difference between the int based learning and the cha based force of will.
Swordmage: There really wasn't any one specific "sword mage" in 3rd, but rather a bunch of sorta-kinda sword mage prestige classes. That was a bummer cuz a) you couldn't be a sword mage from the start, and b) 3rd had this kind of hatred of gishes (and red mages. poor me trying to make a gish that had some arcane and some divine spells >_<). While I wasn't totally in love with the power/spell selection in 4e, and it could have used a second role eventually, the sword mage was the first time there was really a strong fighter-wizard hybrid. (my actual cleric-swordmage hybrid multiclass wizard in 4e is tons of fun and makes for an excellent red mage :D).
Warlock: Never got to see the 3rd ed warlock in action, but from what i hear it was an entirely at-will caster, which is amazingly cool. They did a sorceror one in 4e I think (never saw it played, just glanced through the book). This deserves mention because an entirely at will caster is very neat, and could fit the simple caster concept very well. That being said, the pact system in 4e made for a very intestesting character that really acted different from a wizard, as well as from the other arcane striker (sorceror).
Warlord: Only around in 4e. A great, great class. I did not use it often, and I wasn't as big on moving my allies and giving them extra actions as I was on divine buffs, etc, so I stuck with cleric, but what I did see was very cool. It explored very innovative and useful design space, and rightfully there is a lot of love for it on the boards as well. That being said, a) I know there was a major issue with the concept of 'martial healing,' and b) I do think that the warlord could successfully be incorporated into the fighter as one of the 3 styles I mentioned, and that would give all fighters access to a little bit of battlefield tactics, which would help deepen the fighter in both combat and in character, while still letting diehard warlords take the appropriate class feature to get the healing (whatever form it may take).
Wizard: Last but not least, the wizard. This is another rough one. I think that 3rd most closely captures the wizard people are looking for: the depth and breadth of spells, the destruction and the utility, the great tool kit of useful and interesting spells to try and find the right one for the job. It was a very neat class. It was also very powerful, and that got difficult. 4e reigned in the power, and added at-will attack spells - which was amazing because it let you always feel like a casty wizard - but definitely cut down on the wizard's purview. Some say it was a necessary evil, other that the knife cut too deep (though it seems most agree something was needed). I think 5th/DDN is headed in the right direction: at-will spells, if you choose, to always feel like a wizard; rituals for lots of repeatable utility without that eating into normal spells per day, limited by time and, when realistic, materials; an interesting array of spells to choose from to otherwise fill the slots. I think the concept is there (even without encounter powers atm, as those really can be added in later as a slightly less potent, but reusable spell slot), it's just the math that needs polishing (spell damage #s and effects, and #s of spells, difference between 1st and 9th level spells, etc).