Marvel vs DC settled a major fan debate by showing that Batman is stronger than Daredevil. The 1996 intercompany crossover that allowed fans to vote for the winner in battles between comic book heroes and villains began with a dimensional breach that randomly scattered figures between each universe. While DC and Marvel's characters tried to make sense of these events and what they could mean, one such crossover saw the lethal assassin Bullseye end up in the Batcave, where he quickly made enemies of two of its residents, Batman and Robin.
Despite the companies' famous rivalry, characters such as Spider-Man and Superman had been a part of previous crossovers that took place in a shared continuity where both DC and Marvel's characters not only knew each other but had always worked side by side. The Marvel vs DC miniseries (also published as DC vs Marvel) written by Ron Marz and Peter David with art by Dan Jurgens and Claudio Castellini was the first that saw both sets of characters interact from their own respective continuities. Caused by two omnipotent brothers whose awareness of each other led to a contest of champions to see which deserved to live, Marvel vs DC began as characters disappeared from their usual surroundings or environment to end up in a new universe altogether, with new allies and threats present.
In DC vs Marvel #1, Batman is seen trying to negotiate Robin's safety from Bullseye, who has a knife to Tim Drake's throat and is demanding answers. Disoriented from his sudden teleportation, Bullseye laughs at Batman's attempt to intimidate him with his appearance and name. When Robin escapes his grip, Batman throws a Batarang at Bullseye, which the psychopathic killer catches and quickly redirects toward the fearsome vigilante. But the Dark Knight dodges this which unsettles Bullseye who, like Suicide Squad's Deadshot, claims he "never misses." Batman hits him with one direct blow to the face, and the villain admits, "You hit... even harder than... than... Daredevil," before passing out.
Despite being from separate universes, Batman and Daredevil have a lot in common (to the point that some fans argue they should trade names.) Both have suffered the traumatic loss of a parent, both spent significant time training their body and mind, and both wear costumes that are meant to scare and intimidate criminals. While Matt has the advantage of his heightened senses and radar sense to compensate for his blindness, he's also fought Bullseye countless times. Having hurt Matt Murdock in a way that few villains have by killing Karen Page, Bullseye is not only a threat to Daredevil but pretty much anyone that he comes across. He's absolutely prepared to kill Robin with little thought or consideration, and his experience with Daredevil's signature billy club make manipulating a batarang child's play. Nevertheless, Bullseye was completely unprepared for Batman's training or strength, especially after threatening the life of his partner in his sacred base of operations.
There's an argument that Daredevil may still be a more skilled fighter than Batman, given the way in which his enhanced senses and personal radar allow him to anticipate his opponents and environment, but it's clear the Dark Knight just hits harder than the Man Without Fear. Marvel vs DC may have settled some of its face-offs via fan vote, but in the case of Batman and Daredevil, it turns out the companies agree that Gotham's protector packs more of a punch than the Devil of Hell's Kitchen.