Well, Diana has, depending on the writer, anywhere from hundred to thousands of years of experience training with her sisters. Archery, swordplay, hand to hand, tracking, the art of war in general, and tons of other disciplines have been handed down to Diana from her mother and the rest of the society. Batman's expertise is primarily in detective work, the physical sciences, psychology, stealth/espionage and precision based tactics. If I want to choose someone to lead a team to perform a surgical strike on a highly guarded military base, I'll pick Batman. If I want someone to lead an army, I'll pick Diana.
In terms of fighting ability, Diana's Amazonian style seems to be pretty effective in terms of strikes and grappling (she is Greek, after all). Batman, on the other hand, has accumulated over 100 martial arts. His breadth of knowledge likely exceeds that of her own.
Wonder Woman was de powered and still beat the shit out of the Goddess Diana, who is like Ares' daughter or something. WW's weaker than Superman. And she's had to use skill to be on an even playing field. She used her skill to utterly embarrass Powergirl, who is probably stronger and faster than her. Wonder Woman used her skill to beat the Queen of Fables, who is a high reality manipulator. She's used her skill to beat Zoom. She certainly isn't fast enough to actually beat him. She used her skill to fight Konvict. Who was beasting the whole JLA. She also used skill to fight Ares, Circe, and Amazo. She regularly fights beings who are beyond Superman. The only thing I can think of that saves her a$$, is her skill. She's at least as skilled as Batman. Hell, she once even beat Beowulf with a sword. Who beats Beowulf at his own game?
Batman is unexplainable. He once beat 3 martians at the same time. And those guys, even without their powers, were all crazy fighters with millions of years of fighting experience. He's beaten people far above his own ability and strength.
I'd say they were about equal. Just skilled in different areas. Wonder Woman could beat Batman if it were wrestling, swords, brawling, etc.
Batman wins if it's acrobatics, martial arts, etc.