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).
You have. Download Protonge manually from https://github.com/GloriousEggroll/proton-ge-custom/releases and unpack the archive into “~/.steam/root/compatibilitytools.d/”. Each Proton version has its own folder. Restart Steam then you can use Proton GE from there. Its like Wine GE, but optimized for Steam.
And what games are you playing? You can also lookup each game in Protondb as linked before. Protondb is a database of user reports, with often useful information.