Before anyone asks, the context is that Mr. Mxyzptlk and Bat-Mite are arguing about Batman and Superman, and imagining all this.

Gods, I can't recall if it was a comic piece or one of the shows/movies, but Batman had acknowledged that Supes would murder the shit outta him in any given situation. IIRC he states that the only reason he ever 'won' a fight against Superman is because Superman refrains from genuinely trying to harm/kill him.

That being said, Bats might actually win a battle to the death against Superman, simply because Clark decided Batman's life was more valuable than his own (or somethin' of the sort).