While Superman is obviously more emblematic of the hopeful and good-natured side of America, Batman instead lives in the dark and vengeful side. His motivation seems not to be protection of the citizens of Gotham so much as extending punishment to its criminals, a cause which he pushes all of his physical and financial resources towards. His MO is law and order, and inherited wealth, which when not used for his myriad Bat-gear is used to throw lavish dinner parties and fund his playboy lifestyle (while Clark Kent endlessly pines for his true love, Lois Lane). Now does this, or does this not sound like the archetype of the Yuppie Republican? Isn't it interesting that the current film incarnation of Batman is played by Christian Bale, one of whose previous roles was Patrick Bateman, the psychotic yuppie? Is it that outlandish that in a storyline being developed by Frank Miller (Sin City, 300), Batman hunts down Osama Bin Laden, for isn't that in keeping with his ideas about vengence?
As for who wins in a fight, most comic fans will tell you that depends. On an even playing field Superman obviously has the advantage. For Batman to have a fighting chance (not physical fighting chance), he needs an environment where he can exploit his cunning and planning. Either that or simply find some Kryptonite, though it's worth mentioning that the stuff is kinda rare, it's not like you can buy it at 7-11.
Personally, I think that, although he is dependent on his powers, while Batman depends on strategy, Superman would still have the edge. After all, Superman's most prominent nemesis, Lex Luthor, is human, just like Batman (and also possesses similar if not greater economic resources, as well as comparable genius intelligence), yet even he has never succeeded in beating the Man of Steel. I'm not saying Batman couldn't, just that the odds don't favor him, after all, even having access to Kryptonite never guaranteed Luthor's victory.
I realize some people are hard on Superman, saying that he's only good because he has super powers (forgetting that he doesn't use them to conquer, only to serve), that his weakness to kryptonite makes him a wuss (hey, he's got to have some weakness, and don't forget that he's also susceptible to red sunlight, as much of his power is derived from Earth's Yellow sun) and that he just isn't as cool as Batman (which is probably true). But even if he is cooler and better in bed (obviously into some kinky shit, though there are those that say he's gay), for me it comes down to a simple fact: if Darkseid pushes me over and takes my wallet, I ain't gonna be wetting my pants and screaming for Batman.
