Interesting that both of these characters are willing to kill - Keaton having a high onscreen body count and Arrow going from killing everyone to not killing to back to killing again.
Having said all that, I think that the Batsuit in 1989 was completley bulletproof, so unless Arrow puts one through Batman's eye, his best weapon is not as useful.
In hand to hand skill, it's tough to tell, Batman gets overpowered by a much larger opponent at the end of the film ( and then gets sneaky and kills him) - although I'll say advantage Arrow , because in season 5 he kills Dolph Lundgren with his bare hands.
So Arrow.
Just a thought
@Docker2.0 , because Ezra Miller Flash appears to Grant Gustin Flash during the Crisis it's fair game to pit any movie character against any DC tv show character.
E.g. Henry Cavill Superman vs Tyler Hoechlin Superman or Brandon Routh Superman.