Quality-wise, GOS camera is no different from any other 3rd party camera and is simply a no match to Google Camera as Google Camera utilises all the APIs / hardware whilst GOS camera (and any other 3rd party camera) does not.
So GOS cam (+any other 3rd party cam) vs Google Camera:
Google camera has Night Mode, so if you take a picture at night / dark place, it will make it much better. The GOS cam (or any other 3rd party) camera is not good for night shots as it doesn't have any post-processing algorithms so pics will be too dark. The difference is big and noticeable - try to make a night time pic on GOS cam and Google Cam and you'll spot the difference.
Google camera has post-processing, GOS camera doesn't. This is noticeable when looking at details.
For example, take a pic of a carpet. The stock camera will process it nicely so you will see all the fine details if you zoom in. GOS camera won't (not much details if you zoom in, pic will be blurry).
Google Camera has lots of useful, extra modes (Portrait and Macro being one of the most useful ones), GOS doesn't.
Comfort-wise, Google Camera has pre-set zoom buttons, so you can easily tap on desired zoom level. GOS camera doesn't have this so you have to manually zoom in (which is a headache as takes time + its almost impossible to get fixed zoom (if you try 5x, it will most certainly end up with 4.9 or 5.1).
GOS (and any other 3rd party camera) is good for basic shots but if you really want a quality photography, then nothing can beat stock Google Camera (or modified GCam that is basically the same Google Camera).
Please note that Google Camera (and GCam) are much slower on Pixel 7 vs stock OS for some reason (there is a separate thread about it). Pixel 6 devices are working fine though.