It depends. I'm an Axton Main because I love playing Allround Characters (and I played Roland in Borderlands 1 so I stuck with the Turret).
Lore wise, Zer0 and Gaige. They have cool background stories (but all characters do).
Also, Krieg. His dialogues are just hilarious. I had times when I played with him where I died ingame because his random mumblings made me laugh too much.
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Axton was my main when I played ps3. I do have one on HC, but he's only 44 right now.