You are right about Batman being "a rich bitch with a utility belt and a butler" HOWEVER, he is also EXTREMELY trained in many different fighting styles, extremely acrobatic and incredibly smart.
Superman, on the other hand, is only a super hero because of the sun. Sure, he has super strength, he can fly, has heat vision, x-ray vision, super speed and is damn near indestructible, but he didn't have to work for any of those things.
Obviously, Superman would win a fight, but not as easily as you'd expect.
Batman gets my vote (seriously, read Batman: Year One if you doubt his badassness!)