This sheet is now available at https://docs.google.com/spreadsheet/pub?key=0Auhe1_YgITaTdDAtTTZMNXJ0VUZ3REtVb0VOTXJIZFE&output=html. This is the public html viewable version. Only use the link later in this post if you wish to view the behind the scenes calculations.
I wrote up a spreadsheet to help me get a handle on the relative DPR values between the various classes, and how they scale over the lifespan of a character. Obviously DPR is not the only measure of the effectiveness of a character, but it is an important one. I have linked it here:
The current target AC I use is 18, the highest listed on any monster in the bestiary. I've fiddled with that number and the rankings stay fairly consistent. For all the classes the characters start with a 16 in their attacking stat, which is improved once at level 4, and a second time before level 11.
Feats - I chose not to model any feats. For anyone curious, GWF is stupid good and boosts the damage for anyone who can use it past any other choices. None of the other DPS feats are worth using by anyone.
Barbarian - I modeled: Rage damage, Reckless Attack, Extra Attack, Brutal Critical, Unchecked Fury, and Brutal Rage. GWF is obviously amazing for Barbarians, as automatic advantage makes you crit more and thus get more extra attacks. There is
also a funny thing where Barbarian damage can go down if you increase their attack bonus too much. This is a result of the interaction of Brutal Critical, advantage, and Unchecked Fury. Basically, the damage cost of possibly losing a hit is worth the gain of it being critical. This also helps GWF work even better, since the -5 penalty doesn't actually hinder their damage when they go for extra damage. It's crazy, I know, but true.
Bard - I modeled: Bard Song, and Extra Attack. Obviously Bards don't do a ton of damage, but they do double a Bear's DPS while taking free help actions and casting spells, all in the same round.
Druid - BAREZ LOLZ. Seriously, it's bad.
Fighter - I modeled: Fighting Styles, Extra Attack(s), and Improved/Superior Critical. The extra attacks heavily favor a great axe even before GWF, which is even better because of the extended crit range Fighters get. If you want the DPR for an Action Surge round, multiply by 2.
Monk - I modeled: Unarmed Strike, Flurry of Blows, Ki Flurry of Blows, Supreme Flurry, Improved Flurry of Blows, and Fist of Four Elements. Monks are pretty awesome. They scale well through all levels, they don't rely on a stupid OP feat, they have a lot of defensive abilities, and they have an ability to burst even beyond what I've modeled. Touch of Stony Doom? Man, that is golden if you can get them to fail a save. Monks also have funny scaling points, getting strong damage improvements at levels 8 and 17.
Paladin - I modeled: Fighting Style, Divine Favor, Extra Attack, Oath of Emnity, Magic Weapon(2nd and 4th), and Improved Divine Smite. Paladins put forth some good two-weapon damage as a result of per-hit damage buffs. GWF probably still puts a great axe over the top, but for my money, I'd go with Shield Master, and rock two weapon fighting. Gives a traditional Paladin image and a solid mechanical benefit in the form of +2 AC. More attacks also means more opportunities to crit, and any time you crit, immediately burn a smite for awesome, uncontrollable burst damage.
Ranger - I modeled: Fighting Style, Slayer's Momentum, and Extra Attack. One thing I specifically did not model is Staggering Attack. While Slayer's Momentum only requires a hit every round to maintain, Staggering Attack triggers after you hit for the first time, and only for the rest of the round. It is problematic to model, to say the least. It would help two weapons more, but as has been repeated, GWF is stupid good and probably still pulls ahead in average damage output. I'd still probably just go dual-wield and have a bow for backup/spell casting. Rangers need some love, but if you stay versatile you'll contribute fine in a party.
Rogue - I modeled: Sneak Attack. That was a short list. Rogues don't have a lot of damage mechanics, and honestly, they need something.
One final thing I wanted to bring up was break points. From these numbers and the general layout of class features, there are some key break points to get out of a class, if you don't want the capstone. Barbarians should drop out at 14 or 16, nothing past there increases damage, and 5 rages is plenty. Fighters should drop out at 11 or go all the way to 20. Monks enjoy smooth scaling from 1-20 and get a range of abilities. Paladins stop scaling at 11-12, but want to continue improving their spellcasting, so multi into another caster. Rangers don't get extra damage after 11, but Swift Quiver at level 17 is pretty awesome for swapping to a bow. Rogues, as the class stands, are a 1-2 level dip for a grip of skills, Expertise, and maybe Cunning Sneak, past that they offer nothing to improve your skills or offense.