BL1: Brick. Probably the most underrated character in that game. People keep talking about how Lilith is very OP'd and that may be true but in the later levels, so was Brick since you, you know, pretty much became invulnerable. And seriously, I can't remember how many bosses I punched the shit out of with him, even when they were somewhat out of my league. Don't get in the way of a Brick.
(Oh yeah, and there's a super easy glitch you can exploit with him to make yourself go faster permanently too. I think I may just have been the first one to discover it actually.)
BL2: Can't say I have much of an opinion on this since I haven't played it enough yet but if I had to choose, I'd probably have to stay true to form and say Salvador.