Those familiar with the wacky hijinks of the mid-20th century know that mysterious rays from infernal machines were America's #1 export. You had your shrink rays, freeze rays and the inexplicably popular "Romano Rays." Comics were full of 'em because it was an easy way to create a stupid situation that could fill a dozen pages -- say, like a super-evolved Batman whose huge and diabolical brain hatches a plan to make Superman grow a beard and develop a minor speech impediment. Sadly, that was not a hypothetical.
So Batman, raising the bar for literal and figurative dickheads everywhere, uses his new noggin to go to the future to be with his superior brain buddies. Superman follows him to Tomorrowland and navigates Batman's defenses, punishing his one-time friend with an awkward mid-flight spooning. Taking them both to the distant past, Kal-El supervises the construction of a new machine, then promptly pushes his dickhead (in more than one way) friend inside the mysterious conclude-o-ray. Batman loses his malevolent streak with his super-intelligence, turns Superman back to normal and they both have a long car ride home where they pretend nothing happened but it's really awkward until one of them turns on the radio and it's that one No Doubt song they both really like. Both got their pot shots in here, but we'll give the point to Superman for attempting daring Unabomber look.
Taken together, it's hard to come up with someone or something that could defeat the two most powerful men in the world. At some point, villains figured "Hey, if you can't beat 'em, join em! No, I mean really, we should join Batman and Superman into one horrible uncontrollable abomination of science. It can't lose!"
Depending on the comic with which you fritter away 10 irreplaceable minutes, the horrific technicolor Frankenstein known as "Composite Superman" has a variety of the aforementioned asspull abilities. Besides being split between Batman and Superman, this goober packs powers from such luminaries as Bouncing Boy and Elastic Lad, not to mention a talent for exposition not usually seen outside of a Marvel wiki page. This was a forgettable romp back when it ran in the 60s, but recently the story came back in a dark re-telling.
Today's Batman is totally unfazed by a goon like Composite Superman ripping himself in half -- especially because that was the plan all along. Composite Superman's fatal breakdown was deliberately brought on by Batman, who decided that the only way to deal with this all-powerful creature was to make him want to commit suicide to end the anguish of being split between two personalities. Ultimately, the harrowing event forces Batman and Superman to reconcile just how different they are, and the struggle they face with each other even as comrades. Above all, it's a tragedy with no winners. So, point to Batman.