Originally Posted by Prison Mike
I never got the impression that Clark was a brainiac in the comics. Batman always seemed smarter than him and he's human.
Really depends on the writer. But Superman has generally been depicted as having superhuman intelligence. He's built robots, rebuilt starships, etc. It's usually simply implied that he has superhuman intelligence, like most Kryptonians. Being the son of Jor-El helps. This is more emphasized in older comics, where he was shown to be an outright genius as a kid. I recall in some stories he was also a polyglot (spoke many languages).
Batman's intelligence is generally high, but some writers have turned him into an unparalleled polymath. This is a comic book character, so obviously, the writing isn't going to be entirely realistic, but Batman's intelligence often exceeds that of characters who should be smarter than him (like aliens with literal superhuman intelligence). It depends on favoritism from the writer.
Though Batman could certainly be more cunning than Superman. That wouldn't be implausible.