Round One: Cap take this with some difficulty.
Round Two and Three go to Batman. He fought multiple villains in the Arkham games who are on Cap's level or highery. Solomon Grundy, for instance, was originally a Superman foe who was later moved into the Batman comics, and his strength is far greater than Cap's. Not only that, Batman's feats at taking on multiple thugs while tangling with some of these main villains shows his agility, reflexes and reaction time are far ahead of anything MCU Cap can handle.
Cap on the other hand had his hands full with a regular dude at the opening of Winter Soldier. With a fully equipped Arkham Batman, he wouldn't hold out for long.
Jason deserves his own thread.
