Axel's cool because he's the only character that actually has flaws without being totally obsessed with darkness. He starts out a nasty manipulative pain in the butt and ends up being a slightly more friendly nasty manipulative pain in the butt. But he tries to do the right thing, and fails, and that's something no character in the series that I can think of has done without any darkness being involved (because they're always perfect angels and it's all the darkness' fault they killed people). He's relatable because he's trying to do the right thing most of the time, but he isn't always perfect at it. He does bad stuff and he does good stuff, like a normal person. I would say he's the best character in the series (not coolest, but best).
He also had some character development in that he befriended Roxas and became nicer as a result. Sure it's not all that much, but it's better than most people.
I have no comment on the attractive part...