I have always been a Batman person. When I was an avid comic book collector in my youth I was accused of buying anything with Batman on the cover. Not true (although I did buy this).
A great argument for why Batman is the more intriguing character is presented at BamKapow.com here. You can guess the basic reason: Batman is human and therefore relatable, Superman is basically a God. Alan Moore knew this, and gave us the kind of Superman we could understand in MiracleMan and Dr. Manhattan. As the article points out though, if Superman had too much depth, he would cease to be Superman.
I actually recently heard from a Superman fan the only good counterargument I've ever heard, which went a little something like this:
"Imagine that anything you ever wanted you could just take, and no one could stop you. Any frustration could be dispelled, any desire immediately quenched. You decide not to act on those desires. Now imagine you have to make that choice every second of every day. Most of us don't have the willpower to skip a tasty looking donut even though we know it's not good for us. Now look at Superman."
Does sort of put the debate in a different light, I must admit.