GOG has the benefit of being completely DRM-free and not requiring their application to download, install, or run games. (They have a storefront app, but you can also buy games and download stand-alone installers with a web browser.)

Steam has the benefit of contributing a lot to gaming on Linux, to the point where ditching Windows is now very much viable in most cases. (Games with certain specific anti-cheat systems are the main exception.)

I'm happy to spend money with either of them, for different reasons.

Older games I default to gog. Seems to have better support for keeping them working on modern platforms.

Depends on what you want.

GOG does DRM-free stuff. It also gives you more control over when updates occur (unless a game updates itself and forces some kind of update, GOG won't do that). That probably doesn't matter much for the original Fallout, but some people playing heavily-modded newer titles like deferring updates for a while; you can do that on Steam, but it's kind of fighting the system. Though...I haven't used GOG much recently, so I may be out-of-date on their client software; I just use an open-source Python program to download games. GOG hails from Poland.

Steam "does more stuff". It defaults to pushing out updates. It provides a lot of functionality (like a controller configuration interface, a Windows compatibility layer on Linux that "just works" more than base WINE; I've had a better success rate of things "just working" than with GOG. It has built-in modding functionality which many games -- not Fallout -- use to distribute mods. Steam hails from the US.

I think I may own a copy on both services, myself.

For old games, I'd lean towards GOG. They try to make sure they actually run, and run well. On Steam, it's up to the publisher.

GOG if available, no DRM and while I think they do have a launcher, I don't think it's required. I could be wrong...

Steam does tend to be annoying about logging in and out, not necessarily letting you choose to update stuff, it has DRM and requires internet (or will at least be annoying about it).

GOG is more like, gosh, downloading some software and then running it. Without it doing 11 kinds of random shit on you.

Whichever version mods work better with. E.g., widescreen support