I don't think there's necessarily a right answer here. If your paramount goal is security, then you're probably better off using Google Play as much as possible. While far (light years) from foolproof, Play Store is adding some additional verification and security checks. Take, for example, a scenario in which a "good" FOSS app is taken over by a nefarious actor (either because they simply paid off the original dev like we've seen with browser addins, phished the dev, or whatever). That bad actor would also need to compromise the dev's Play Store account and then evade the automated checks Google runs on Play apps.
Obtainium is an awesome app, but its approach to updating is still more brittle than something like the Play Store. APK naming can change, and some of the more complex approaches can break without warning (e.g. Firefox has changed where it stores raw APKs in the past), so you need to stay on top of that. If you've got a lot of apps, it'd be easy for some to fall through the cracks.
That said, if your primary goal is privacy, then the calculus changes, and avoiding Google becomes more important. There's also the factor (not very important to me, but relevant for some) that many developers who release apps on Github or their own sites do so at the same time they submit them to Play, which means you get them faster going direct. As @n3t_admin said, some also provide better/different versions (as an example, I get Librera from Github-via-Obtainium instead of Play because the dev makes the pro version available for free there).
Personally, I have just accepted that a) I simply can't live a sufficiently convenient life with a no-Google phone, and b) that I'm too lazy to go with the multiple profiles approach that more hard-core users advocate. To the extent that I'm going to have GMS and Play on my phone, I might as well just take advantage of the added security and elegance of a centralized updated system, so if I can get an app via Play, I usually will.
(Although I do have a Pixel Tablet that I use solely for web browsing and videos, which has very few apps and no Google services it all. Almost everything on it updates via Obtainium. It works great, but it's only got a handful of apps. Amazing battery life, though.)