The big advantage Stadia has over GeForce Now is that for GeForce Now you have to have a machine capable of playing those games in the first place. If you have a great gaming PC, then Stadia probably isn't for you.
Edit: I was mistaken. i was thinking on nVidia GameStream feature that allows you to stream from your PC to Shiled in your home.
You’re mistaken about GeForce Now - it streams games running in nVidia’s servers. If I remember correctly, based on Intel Xeon and their own Volta GPUs.
GeForce Now has its own library of streamable titles for purchase, but it also allows you to link your Steam (and others) account to authorize streaming of games you already own and happen to be available in their library. But they run remotely.
I was very impressed with it, and my comparisons between streaming from nVidia’s remote servers or my own gaming PC yielded negligible differences in visual performance and latency. Your mileage will naturally vary.
This. You don't need a PC at all, I don't have one, just a TV and a Shield, and GeForce Now works great for me. I just buy Steam games through their website and it works perfectly.
It does not look like I can use it from either my Chromebook or my TV (Roku or Chromecast), where as Stadia indicates that it will be playable on my Chromebook, Android phone, and Chromecast.
Edit: I was mistaken. i was thinking on nVidia GameStream feature that allows you to stream from your PC to Shiled in your home.