Best all around? I'd say Maya. Phaselock with Ruin/Converge and the right gun, she can take down a wave of enemies every six seconds with my set up. Along with her support role with Res, Sweet Release, and Restoration, she can keep a party at high health and instantly revive from FFYL.
Best dps and survivability I would give to Sal. Crazy health tank mode domination during gunzerking, crazy damage if wielding a slagga in one hand, and double grenades/gunzerking while FFYL? Just try to stop him!
Won't change this sig until the next time I change it 4/15/2011
The problem with these threads is that most are probably going to say the characters they're most familiar with are "best".
I think based off of everything I read and what I've experienced so far with Zer0 and Gaige that the spread of advantages and disadvantages amongst the characters in UVHM is pretty even for the most part.
Axton and Maya have easy slag abilities made better with the 11 levels. I do think personally Axton probably has the most newfound freedom with builds too now but that's just really on paper guessing.
Zer0 can double debuff (death mark kunai+slag shot before deception), and deception makes slow but steady progress just so safe. I average 5 million execution damage with a rapier off of slag/death marked enemies now and that's without the LT, Hide, or Death Blow.
Salvador seems to be his usual so good it's braindead self I can't imagine him not being even better now, though I resurrect a LOT of Salvadors so his worst enemy remains cocky players.
Anarchy Gaige is still amazing, and she has more leeway into other trees at the same time now though. Don't know if much has really changed with her.
I mean, you could argue some characters are easier than others and I've heard some old playstyles (like pure sniper Zer0) have become more limited now, but I don't think there's really a clear cut top tier character or really obviously disadvantaged character. Depending on the gear setup everyone seems to be wrecking the new mode.
There is no "best" but how you have your characters set up that compliments the equipment you are using. As I have seen videos people soloing/co-op Raid Bosses (on the GBX Forums) 1-shotting on TVHM/UVHM.
Ultimately, you just have to find what works well for whoever you are playing with. Otherwise, n00b friendly characters/skills could be classified as "best".