I'm having no compatibility issues with the new version of Classic for the most part, though the HR method can be a bit more of a hassle to set up than the original patch for some cases. That got solved eventually though.
Mod-wise, I'm going to quote what I posted in the mod thread:
I'm having problems with Fallout Fixt and the new "classic" version of Fallout.
I also had this with FO2 and the unofficial patch, however I tried again and this time I didn't let the UP install it's High-Res patch. It works perfectly fine.
I suspect the same with Fixt, however there's no option to install it without HR.
EDIT:
brothergl00m: I never had much trouble with Fallout 1, I could play the game start to finish without any CTDs.
Fallout 2 on the other hand has crashed on me ever since I had it on physical copy. It's just an incredibly unstable game and I don't think it matters which copy you're playing on, it's gonna crash. Usually when you forgot to save and you lose an hour of progress. Hence why I still haven't actually beaten that game haha.
If you're having problems with FO2 try using the unofficial patch. For some reason it fixes problems of it not running for when I had it with the new version. I'm not sure what Bethesda broke, but it must've been either minor or pre-existing.