Actually, compared to Batman, Superman would be of a child-like intellect. Batman is literally one of the smartest people in the DC universe, and is rarely if ever outsmarted; particularly when it comes to tactics, battle plans, strategy, or combat.
Without comparing education and academic backgrounds but just pure raw intelligence, on the Marvel powers scale, Batman's intellect is similar to Tony Stark or Bruce Banner (5/7). Batman is smarter than Peter Parker who is a genius-level character.
Literally, he's
that smart. That's why he's so badass. He's not just a tough guy in a suit.
I agree with the premise here because you're saying Superman is after Batman and Batman is being caught spontaneously and off-guard. Totally agree, Superman wins.
But in this movie, and like in the comics, you'll most likely see Batman coming after Superman - or at least, knowing that Superman is coming and having time to prepare.
That's the key difference.
Once Batman has time to formulate and develop a strategy, there are maybe a handful of people in either the DC or Marvel Universes that could stop him...
Also, Batman has been known to carry Kryptonite in his utility belt at any given moment. And keep in mind, the movie and the comics generally portray Batman being the one to have to prep; Superman is simply not aware of just how resourceful Batman - not until the Justice League is formed.
A multitude of ways.
Kryptonite kills Superman the same way exposure to high levels of radiation would kill you or I; it's a slow process, but in time, yes it will kill him.
However, the immediate and most important effect of Kryptonite is that it
depowers Superman.
Once Superman is just a man, hell even if he is only somewhat depowered, he is absolutely no match for the world's greatest fighter.
None.
Crafting handcuffs made of, or coated with, Kryptonite would completely depower, incapacitate, and eventually kill Superman.
But here are some things that Batman can do to combat Superman based on things others have done in the past.
1)
Kryptonite - vitally important.
2)
Biosuit / Exo-skeletal armor - think Iron-Man or better yet the Hulkbuster armor designed specifically to fight someone of similar strength to Superman.
3)
Metamaterial based coatings - completely neutralizes Superman's x-ray/heat vision.
4)
Teamwork - see
Wonder Woman. You might think, she's garbage; but she is bad-ass.
5)
Poisoning - Batman could use Poison Ivy's poisons to subdue Superman (it's worked before, and he has a catalog of her serums on file).
6)
Tech - Batman had developed a plan to disease Superman so that his skin would be transparent to solar rays - depowering him permanently.
So yeah, I mean I get what you're thinking; if you put these two guys in the Thunderdome, totally unprepared, only Superman is likely to walk out.. I think that's a given. But that scenario is unrealistic.
Again, with preparation time, Batman > Superman.