Different weapon damage dice is dumb to me. A dagger specialist should be just as viable as a greataxe wielder without needing some fiddly feat chain or prestige class to make it viable.
ALL weapons should generally use the same damage dice (or the rough equivalent with another die type), but should be differentiated via other mechanical traits. For example, a greataxe might allow you to reroll 1's on your die, while say a dagger gives you an +4 initiative bonus or something. That's what I want to see.
In AD&D speed factor mattered a lot. So a dagger doing a d4 was offset by the fact that you'd almost always strike first, before any big weapon user or spellcaster. All that was lost when 3e removed speed factors but didn't replace it with anything. It created a whole class of weapons that were flat out superior to other weapons with no offsetting mechanical factors. That was a big mistake, IMO.
A lot of people like 3e for its simulationist aspects, but IMO, this even fails in that respect. In the real world, shoving a dagger in someone's gut or hacking at them with an axe is equally lethal, so there is no legitimate justification from either a gamist or simulationist standpoint to nerf dagger damage in respect to axe or sword damage without providing some other offsetting mechanical benefit.
Also damage between melee and casters needs to scale with level. 13th Age solved this problem nicely, and Next could do a lot worse than to simply copy their mechanic of adding a die of damage per level (which itself came from 4e). Though static damage bumps work just as well for people who don't like to roll a lot of dice.
One reason (among many) that LFQW became such a problem in 3e is the damage discrepancy between warrior's and casters in terms of damage output at higher levels because damage didn't scale equally. There is no legitimate reason that a badass fighter shouldn't be able to cleave their way through lesser enemies in the same way a fireball can clear a room. None. Even in history there are stories of great warriors cutting down lesser warriors with ease. Let casters keep their flight and supernatural effects, but when it comes to melee combat, the fighter should have no equal.
For example, if a high level spellcaster is throwing out 10d6 fireballs at whatever level, then a fighter of the same level should AT LEAST be doing say 5d12 (or 1d12 + 26) damage with their weapon of choice along with whatever other traits their weapon has.
My two cents.
