TL;DR - If Hawkman fought Batman in a stand-up fight, he would defeat Batman with relative ease. In addition to being stronger, possessing regenerative powers, greater speed and the ability to fly, he also has a wide range of lethal weaponry.
The standard response to this argument is that if Batman knew a fight was coming, there's really no-one he can't defeat, up to and including Superman.
Batman fought Hawkman in JLA #119 as part of the "Crisis of Conscience" story arc. Since Batman was under Despero's mind-control, Hawkman wasn't looking to kill him but merely subdue him. Batman ended up slugging him and Hawkman backed off. Despite taking a solid punch right in the face from Batman, on the following page Hawkman seems quite well, albeit rubbing his jaw.
They also fought (briefly) in Public Enemies. Again, Hawkman has a substantial advantage, trapping Batman in a thrown web but doesn't move in for the kill, ultimately losing when Superman steps in.