Well... Let me answer this with how I think four different super heroes would handle a drunk picking a fight with them in a bar, and I mean just your average ordinary schmoe that goes up to them and says, "I bet I could kick your ass." 
Superman: Supes would look the guy up and down, smile, then say, "Who knows... Maybe you could?" Then he'd fly off because he doesn't care what this idiot thinks and he doesn't want to have to take this guy to a hospital to bandage up his broken hands. Now if this guy had started something with another patron Supes would have interceded and made that guy look like a fool. But he doesn't have anything to prove.
Batman: Batman would take a step back, stare that guy right in the eye and say, "I'd like to see you try." And then just wait for whatever comes, but his assured confidence alone would probably make that dude urinate himself anyway. 
Spider-Man: Spidey would start trying to joke and deflect this dudes aggression to placate him even though he could pulverize him to within an inch of his life with one arm webbed around his back. In a lot of ways Pete still acts like that picked on high school kid before he got his power. 
Wolverine: Old Logan is the only one that has a two track response. He'd either A. Grin, finish off the mug of beer he has and then swiftly kick that guy in the nuts, or B. Grin, finish off the mug of beer he has and then leave out the front entrance... Then a couple hours later when that dude is fumbling around looking for his car keys in a drunken stupor Logan would reappear and then give him a swift kick in the nuts. Point being, either way... Logan is kicking in someone's nuts. 
