If you use the free version of Stadia, it's the same resolution as GFN. If you're a monthly subscriber, the picture quality is much better than GFN because GFN doesn't support resolutions higher than 1920x1080. GFN is REALLY frustrating if you have a 1920x1200 or 1440p monitor. Because of this, GFN can complement my gaming PC (like when traveling with a crappy laptop) but never replace it. Stadia probably could replace my gaming PC if I was willing to buy the subscription.
No waiting period (its rare, but there's occasionally a wait for GeForce Now even with the founders edition)
Games don't disappear from the service like they sometimes do with GeForce Now (granted, if a game you bought disappears in GFN you can still install locally so this may be a win for GFN as long as Steam's cloud saves don't glitch on you)
Stadia doesn't require you to install a 200 megabyte app (assuming you already have Chrome installed)
GFNs video clip feature is a bit buggy for me compared to Stadia although I haven't used those features enough to tell if GFN is consistently glitchy or if I'm just unlucky with the NVidia overlay
The UI for GFN feels clunkier to me but I suppose that's personal opinion. It feels more like VPNing into a really locked down PC, where you'll hear Windows sound effects when there's errors and if a game crashes you're stuck with a Steam error and you have to restart the whole app and wait in a queue to play again. Stadia feels a bit more well-integrated to me.
Stadia also doesn't have to pay the Windows tax
One advantage is that you can play Cyberpunk for free on Stadia (after you purchase the game, which you also have to do for GFN too). Also, last I tried GFN, it seemed a bit clunkier (it felt like more of a "PC on cloud" that you managed, vs a built for web service).
Disclaimer: I work at Google, though not on Stadia.