They should for most. If the games are on both Epic and Steam you can check protondb.com to get a general idea of how well it will run, for any games that are only on Epic, I’d recommend doing some quick searches to see how much luck people have had getting them to run on steam deck/linux. Most games for me have worked perfectly fine with similar performance as Windows, and installing Windows on the Deck is still an option for the games that don’t.
As for the alternatives to the Steam Deck, I wouldn’t go for them over the Deck personally, but I have never used them. I would think the games that have been optimized for the deck would run better on the deck than the alternatives due to its popularity. I might consider them if they were a good bit cheaper than the Deck though and it was a good deal.
Edit: I should also note that I play on a Linux Desktop, not the Deck, but aside from the specs difference the games actually working or not would be almost exactly the same between the two because of how Proton and Wine work.