Maya is hands down my favorite, reminds me of the Adept class from Mass Effect with Phaselock. High survivability (healing Phaselock), really cool character design, definitely the best of the three in my experience.
Zer0 was my first played character since I lean towards rogues/stealthy characters (and I like the fact he's melee-centric with sniper rifles). I find him fun but tends to die a bit too easily (although he gets better with levels and careful playing).
Didn't like Axton much. The turret is great but without turrets this guy just dies (and turrets take long to recharge). Spent more time dying than killing people as opposed to Zer0 and Maya.
Haven't played Salvador or Gaige yet. --- Vixen, Black Canary, Star Sapphire, Circe, Steel and The Huntress for Injustice: Gods Among Us Poison Ivy for Injustice: Gods Among Us DLC
I prefer Sal. Dual weilding may sound boring but I like in-your-face, spray and pray method of defeating my foes.
My least favorite is the assassin. I know he appeals to a number of people but the melee/sniper aspect is wasted on bosses like Bunker or Warrior. I know there are other ways to play but it just didn't appeal to me. --- Fact because it's science. ==============================================