Batman is a better fighter then Punisher, thats a give in but it isn't like he wont be able to keep up. Batman will have the edge at the start of the fight but he's odds go down hill from their. Frank's damage soak is insane and his endurance is top of the line as well, he just wont stop coming. In the end I think Frank would come out on top.
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While the crossover was not poorly written or drawn in the technicale sense of the word. It;s treatment of character was poor in places. Mostly on the Punisher side. In other words Batmans jobber aura seemed to be running on over drive even filtering down to Robin.
One needs only look at the opponents the Punisher fight to realise Batman punking him out that easily is border line idiocy. After all the Punisher can go hand to hand with Captain America, Dardevil, Wolverine, and even Spider-man all people that are at the very least more or less equal to batman.
The Marvel Encyclopedia rates his durability and fighting skill higher then Daredevil.
The other thing of note in the fight described above is that it ignores the events that transpired before it. Which included a major gun battle. For Which Castle was ground zero and Bruce came in latter and stayed above the crowd. I'll give that Wayne did take some bullet to the chest however with is tech and resouces bas armor that could shrug this off is not suprising. I can't remember for sure, but Frank may have been bleeding at this point. Also they had a previous encounter not to long before this one, it was a matter of days I think. In that fight the Punisher was more or less holding his own until the building they were fighting in collapsed around them. Even if they had bothed sustained injures in the afore mentioned collapse, which may not be the case given the armor and gear on the Bat suit, Batman is still going to get better medical care. You only have to look at the fact that the Punisher walked away from a fight and a chance to kill the Joker to realise he was far from 100%. The earlier fight is a better representation of it would go.
As much as I hate to say it Batman is probable going to win. Why comic convention. If this was well handled and the characters were treated with respect and it adhered to their abilities. This could make a great comic and an epic battle.
How can you call anybody, but Batman self centered in a thread that pertains to Batman? Batman is by far the more egotistical self absorbed hollier then thow of the two. Come on more often then not even in Bats own comics he is played as a self centered raving ego-maniac.