Movie Punishers were horrible. Pred takes all 3 rounds. Without Prep Bats can't take a Pred. It was evident in the first crossover against Batman that without info and prep, what he carries standard with him wasn't enough to get the job done. If he had some time to study up on the Yautja like he ended up having in the comics, then he would win by being smart about fighting.
Round 1 Punisher for sure.
Punisher with prep has emberassed the Avengers, Keep sentry from capturing him, beaten ulik (a Thor villain), and beat Spider, DD, and Wolverine together!
Punisher wins with the human gear of HVGs, Anti Tank Weapons, and Armour Pircing or SHIELD Tech grade guns.
LOl at anyone who thinks Pred beats Punisher who has taken 20-100 toner hits and kept going.
Round 2 Predator.
Round 3 Depends. No prep I give it to punisher in all honesty since New 52 Batman is the weakest and realistic Batman ever so far.