I think this is similar to the Hawkeye vs. Bullseye thread awhile ago. Though Ollie has nigh-perfect aim, and can be fairly ruthless at times, Bullseye still has him. In his hands, everything is a weapon, one time the Punisher threw a grenade at him, he threw a toothpick at it and plugged up the pin hole so the grenade couldn't go off. That's just crazy skill. He takes it.
And one time Bullseye threw a batarang at Batman and missed. GA is supposed to be Batsys equal. So I think GA will take Bullseye out. Batman didnt have any problems with Bulleye. And dont say crossovers suck cause if you feel that way dont post and reply crossover fights.
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"I am not afraid of the dark the dark's afraid of me"
I don't know Green Arrow, but Bullseye's a queer so I give it to GA. Plus if snoopdogg is a Batman fan and he says so, I'll agree, cause Wayne's the man.
But down to brass tacks. Yes, Batman is ridiculously good. If anyone can dodge a throw by Bullseye, without any type of enhancement, it would have to be Wayne. I like GA, and he does have various extraneous tricks up his sleeves, but principally he uses a bow. However, Bullseye can turn anything into a weapon, also with his adamantium skeleton he's a bit more durable than old Ollie. Unless we want to make it Connor, whose fighting prowess, I've read, is supposed to rival that of Batman's. That would be a great fight surely, yet I still back Bullseye. It could happen either way, this is just my stance.