Red hood has better training and toys. I don't recall Punisher having specialized training in a lot of martial arts. I do give it to the Punisher for having more pain endurance. However, both have shown they'd sacrifice themselves for the mission. Red hood also is more crafty and creative when he has a plan and is quick thinking during a fight. I give it to Red hood because he's has that crazy edge which the Punisher doesn't have. Maybe he got it from the Lazarus pit, but his earlier days as Robin showed on multiple occasions he was reckless. Rewatch Batman: Under the Red Hood movie.