Frank Miller's Batman would probably think "the hell with everybody" and kick Superman's butt.
Frank Miller's Batman DID kick Superman's butt. BTW, has anybody else noticed that for a guy with unlimited strength and who is invulnerable, that Superman gets his @ss kicked more than Walter Mondale? I mean, that guy would lose a fight with Archie.
The only Super hero that gets his @ss kicked more than Superman is Daredevil.