In the movie "Battle of gods" Goku doesn't seems to be far from Beerus. Later Akira Toriyama said that in Battle of gods if Goku is a 6 Beerus is a 10 and which is a 15. Later we see Goku to attain another transformation (probably stronger) since in the manga is shown as a next stage (in the manga he uses regular god form instead of SSGSS for saving energy probably). In the anime we see Goku using SSGSS Kaioken x10. That would make Goku to be a at least a "60" when Beerus is a 10, unless movie, anime, and manga are all independent stories. Then my question is, is Beerus still stronger than Goku in the series, is he not, I am missing something?
Well, right now I think we can say almost. Due to Whis' explanation of the Ultra Instinct transformation. In the battle between Kefla and Goku. Whis states that Goku's attacks are ineffective because he still hasn't mastered the art of the unconcious attack and also states that it is very hard to learn and that even Beerus hasn't mastered it's use.
If Goku is able to complete it then for sure he will be stronger than Beerus for a moment. He still doesn't have stamina to maintain the form (a common thing now with every transformation).
But given the nature of how it works. I think Beerus wouldn't be able to land an attack on him at full power even with Ultra Instinct active.
Still it's only speculation at this point.