Serious question from a casual super hero fan. Without a boatload of Kryptonite how does Batman even stand a chance against Superman? Batman's just a guy in a suit with some fancy toys, Superman is the real deal.
Batman is supposed to be a lot smarter compared to Superman. So he competes using his mind, tactics and his knowledge of psychology and human nature.
Also, in the comics, Superman has a code where he will never use his full strength because he will kill people. He has violated this a few times, though but it is rare. This is one reason, a lot of folks did not like the last Superman movie, because he killed so easily and damaged Metropolis beyond all reason.