This is Batman vs Captain America vs regular equipment discussion.
Google AI Overview indicates that Jason Todd Red Hood's knife and slashing equipment have been able to cut through and make Bruce Wayne's Batman suit protecting the skin bleed through. If Captain America is capable of parrying Baron Zemo's hand to hand blows where Zemo's karate chop sliced the top half of a garbage bin with a singular swing of his arm. Imagine if Captain America landed that kind of karate chop blow to batman's throat and clavicle and how his knife edge hands would be useful weakening Bruce Wayne's suit. Captain America can disarm Batman of his utility belt with his Shield, it's made of vibranium and adamantium the strongest metals, it wouldn't be that hard. Captain America's brain reacts and processes faster than Batman. Th3birdman15 states Captain America is arguably a more skilled fighter than Bruce Wayne who he thinks only learned the hundreds of martial artists but hasn't mastered them in a way Captain America does. Death Battle content creators Wiz and Boomstick cheated giving Batman equipment from the Arkham Asylum games which are not part of the mainstream earth prime comics continuity. This is proof Wiz and Boomstick are fence riding grifters only in it for the fixed boxing matches to put up their own rigged dark horse to appeal to the fans that are popular with that character or angry their character lost, which is a case of Bardock vs Omniman, Bowser vs Ganondorf followed by Eggman vs Bowser and the second Mario vs Sonic fight after Mario lost the first one. Rigged matches to make the loser or in the former Omniman's case the winner.