No, should work for every game with save files. I think you mean something like the account system in Destiny with internal login. That is definitely not necessary.
My last example was TMNT: Shredders Revenge. Played it on GamePass, bought it later and have all my save files. Other example: Nier: Automata, same thing. That one is no longer on Gamepass and I still have all my save files I started while playing on Gamepass
Like others said, driver support for console controllers is pretty good through the board.
My suggestion: try them out, maybe in a local store on their demo stations (pretty regular around here at least) or by ordering and returning the one you don’t like.
I personally like the controller layout of the XBox controller more than the PlayStation one. But it comes down to preference. So definitely test drive to find the best suit for you.