So here's how I'd make the dynamic between Superman and Batman more interesting: I'd turn them into Lethal Weapon.
Superman is the cautious one, the straight arrow who does everything by the book despite (or because of) his almost limitless power. Batman is the crazy, out-of-control risktaker who keeps dragging Superman into situations he's not equipped for. Batman is the guy who sends Superman and himself diving into a black hole on a spaceship with one dud engine. He's the one who drags Superman and himself into a nest of trolls, whose magic weapons can hack Superman to pieces. He seems to make impulsive, rash decisions, but always turns out to have a plan. Sort of.
And yes, I know that since Grant Morrison's JLA Batman has been portrayed as the uber-control freak who always plans twenty steps ahead in every situation. But he's also the non-powered guy who dresses up in a bat costume, with his face unprotected, and jumps off rooftops into gunfire every night of the week. He's the crazed, half-suicidal Mel Gibson to Superman's Danny Glover.
As crazy as this sounds, it might actually work if the tone is done just right. I can't say that I'm a huge fan of comic books in general, but I'd probably read this just for the "what the fuck was that?" factor.