Actually if I remember right, Batman and Wonder Woman did go round and round in an official comic, and batman did win. There was a comic series where batman was forced to take down the Justice League by himself, he even managed to beat superman. It took months of planning and preparing though.
Without any time to prepare for it, Wonder Woman would probably beat him as skilled as he is, he'd have no way to counter her super strength or powers in his normal day to day crime fighting kit. If he had time to prepare, he'd win, as he knows her powers and weaknesses. He keeps exhaustive records on each of his allies in case hes ever has to fight them.
That was Batman's real strength, he was a detective. He had the information and resources.