I would say they don't trade blows. Gcam is categorically better in image production. Understandably. But by using gcam on your main profile you may risk privacy-loss (unverifiable). And using it on a second profile is not as convenient as is normally expected (have to switch profiles each time).
Google photos is not required for Gcam to take pictures and do its image processing. Gcam does all its processing internally. This includes detail enhancements, white balance adjustments and other color normalizations to compensate for potential flaws in the hardware sensor itself (and other improvements).
Google photos adds options for "post" processing, such as adding filters, adjustments, magic eraser, and other features. It also allows you to immediately review the picture when Gcam is open.
GrapheneOS cam is really good enough for normal picture taking needs. But if you want "beauty" shots or just generally top quality art shots (nature, family, portrait, art, etc) you're better off using Gcam, which is nicely available on GrapheneOS (thanks to GrapheneOS team efforts).