In practice, the difference is negligible.
I'll give Rokr props, though, for being astute in his observation that, technically, "How are you?" questions the 'are' (= state of being); whereas the 'how' in "How are you doing?" questions the Continuous Tense ('are ... doing'). However, like I said, in reality the difference is as good as absent:
"How are you?"
"How are you doing?"
"I'm doing fine!"
("I'm doing GOOD," btw, often means 'the things I do in life, like work, business affairs, are going well.')