Who would win in a fight between Batman and Superman?

Just two days after Action Comics #1 sold for a million, Batman beats Superman by 75,000 dollars. Most of the news outlets are reporting with some glee the 10 million percent inflation since 1938, but a lot weirder is the 1000 percent since the early eighties, when either comic could be had for the difference between the two records. And just a mere 10 years after that, prices had gone up enough that by publisher's(mostly image) clever attempts at cutting print runs and driving up cover prices with exclusive foil-embossed covers, which are now worthless. I own a couple, but thank god I never cared enough about wetworks or WildC.A.T.S. to fall for that. Even more horrible, the four million near mint copies of the death of Superman, bought by would-be collectors the last time the news reported on comics, that awful story won't even be scarce in the twenty-third century.