It's quite different though.

PSN:

• you get access to the "claimed" monthly free games as long as you have subscription
• you can't download or keep playing the "claimed" games if your subscription expired.
• those claimed game will shown as "in library" and can't be purchased even if there is a on-going sale.
• if you paid for a plus member extra bonus discount game, it's still yours if your sub expired.

Epic:

• you can download the game and keep them somewhere, as long as the auth token can verify you own the game and not expired. (similar to Steam I think the token is valid for a week if your internet goes out. it will ask you to go into offline mode as well. )
• this works for both free game they gave out and the one you paid for with money.

I don't know how the higher tier of PSN and GamePass works regarding the access of game you "played".