Has anyone looked at the numbers if you assume +1/+2/+3 weapons? I would think those balance things pretty closely.
I have, sort of.
Remember, a +1 weapon has the same rarity as Gauntlets of Ogre Power (more important if your game allows item crafting or item purchasing I suppose).
A +2 weapon has the same rarity as a belt of hill giant strength (Str 21)
A +3 weapon has the same rarity as a belt of fire giant strength (Str 25) or Stone/Frost giant strength (Str 23)
So your high end Fighter with 2 +3 weapons has nearly as much gear as a fighter with a +3 greatsword and a belt of fire giant strength (though, to be fair, we'd have to pick out a weapon that has attunement ... (While looking for a weapon, I found the scimitar of speed and I'm very upset now ... hahaha ... but I can't find a good very rare weapon to give a TWFer that would especially benefit them, so lets just stick with the +3 weapon).
So, lets say our fighters are above 11th level (we're giving them two very rare items after all).
Two weapon fighter has 4 attacks at +12 to hit and 1d6+8 damage (46 potential). Greatsword fighter has 3 attacks at +13 to hit and 2d6*+9 (52) and an increased chance to hit, or 3 attacks at +14 to hit and 2d6*+10 (55).
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TWFing starts out better than GWFing for a Fighter until 5th level, falls behind but is okay from 5th to 10th, and then dies at 11th. Barbarians are better off not until they can rage every fight, then it's better to. Monks have built in TWFing. Paladins are okay, especially if they can get the style, because of the way Improved Divine Smite works. Rangers who want to use Hunter's Mark do okay depending on their subclass (some subclasses fight for their bonus action). Rogues are good TWFers but it kind of ties into their Cunning Action.
Balancing TWFing would require more changes (like going in and changing how Hunter's Mark/Hex work) than many are prepared for.
Maybe 6E will get it right. Or a few of us will get off our butts and put together D&D Tactics.