SSG Goku being in a world of power he never knew existed would imply the gap between the two to be ridiculously huge, given Goku somewhat implied he hadn't reached his peak and could get somewhat stronger through training prior to the God ritual, yet not enough to match Beerus.
I'd assume all versions of Goku and Vegeta would be part of this "world", including Less than 10% SSB Vegeta who isn't much stronger than SSJ Goku at the time of the U6 Tournament, so Post-God Base Goku would likely be the same and therefore above SS3 Vegetto even with just manga feats.
Manga-wise, the gap between Post-God Base Goku and BoG SS3 Vegetto is at the very least a 1.25-2x one imo and potentially far higher. For SSG, a 30-50x gap at least via scaling. Anime-wise, the gap's easily wider due to Base Goku's feat of being able to put up a fight against Initial Anime hit and contend with a version of Beerus who's state of mind likely made him far less suppressed than the version who beat MY BULMA! Vegeta. As for SSG, the SSJ multipliers are far higher in the anime prior to the ToP based on Gowasu stating the gap between Base and SS2 was several dozen times. If you bring in GT comparison to either, both gaps would get even higher when considering GT top tiers are on the low end of Multi-Galaxy level, whereas Post-God Goku's lower forms have feats to place them on the high end of Multi-Galaxy+ level via scaling.