Both of those superhero games will be excellent cooperative titles.
One thing to be aware of that is somewhat annoying but understandable… if you wish to play a PS5 version of a game together, you must both be using a PS5 DualSense. You can use a PS4 controller for any PS4 version of a game, it just won’t work with PS5 games.
I learned this trying to play It Takes Two; perhaps the best co-op game ever.