While there have been a few instances throughout their respective comic book careers where the Batman proves it.
Daredevil and the Punisher first cross paths in Daredevil #183 by Roger McKenzie, Frank Miller, and Klaus Janson, in a fight that rages all the way through to the next issue. The Punisher starts off strong by shooting Daredevil in the torso, putting him down for the count until Daredevil comes back the following issue and defeats the Punisher. One of their following encounters was in Daredevil #4 by Chip Zdarsky and Marco Checchetto where Matt proves his unquestioned superiority. Frank saves Daredevil from being arrested and brings him back to his hideout where he tells him that the two of them have now become one and the same since Daredevil accidentally killed a criminal. Daredevil replies by showing him just how superior he is to him in every conceivable way. Daredevil steals two of Frank’s guns and uses his sonar vision to perfectly hit every piece of explosive in his hideout with every shot he takes, proving to the Punisher that if he wielded weapons, Daredevil would be unstoppable.
While Daredevil’s actions in his latest run seemingly put the topic to bed in of who is more skilled between the two, Batman hammers home the point in Punisher/Batman: Deadly Knights by Chuck Dixon, John Romita, Jr., and Klaus Janson. In the issue, Punisher travels to Gotham in pursuit of one of his greatest villains, Jigsaw. When he gets there, he is immediately met by Batman who absolutely detests Frank’s vigilante methods and launches an attack against him after witnessing the Punisher execute a number of known criminals. While fighting, Batman says to himself, “Punisher’s tough. Strong. At heart he’s just a brawler. All rage and brute strength.”
Based on Batman’s assessment of the Punisher’s fighting technique, he is in no way on Daredevil’s level in of hand-to-hand combat. Sure, the Punisher may be able to snipe Daredevil from a distance or use a device to incapacitate him as he did in Punisher #3 by Garth Ennis and Steve Dillon, but he is so far behind Daredevil when it comes to fighting skill it isn’t even a contest. Daredevil has heightened senses and ninja training. He can ‘see’ everything around him and can effectively tangle with a horde of criminals all at once and swiftly defeat them using nothing but his fists and perhaps his billy clubs. Because of the superpowers he possesses, the Punisher’s ‘brawler’ fighting style just doesn’t cut it when compared with someone like Daredevil–something Batman knew after one fight with him.
While he is a deadly vigilante and has earned a few victories over Matt in the past, when it comes down to who is more skilled, the Punisher will lose to Daredevil every time, and Batman proves it.