What games? Which Steam Proton and Wine-GE versions do we talk about?
BTW there is also a Proton GE and you can use it in Steam as well. Just saying. Some games do need a specific Steam Proton version, either an older or newer one, such as Proton Experimental. Some games are only working with Proton GE (or Wine GE).
And you can always lookup if the game works, by looking into reports from Protondb website (user generated).