If this was Batman vs Comedian then it would be a bit more even....while Batman would easily beat Comedian in a straight up fight, Comedian cheats ( he'll pretend to be hurt, ask for mercy and then shank you) and Batman doesn't kill his opponents. Batman's sense of morality would be a big disadvantage.
In contrast CW Green Arrow doesn't have a problem with killing ( well once in a while he adopts a no killing policy, but then drops it as soon as he needs to) he kills a lot of people, he killed Dolph Lundgren with his bare hands. In my book that makes him up to the challenge of taking down Comedian, because as soon as Eddie looked like he was going to pull a gun Ollie would put an arrow or three into him.