You'll notice with 60p and 120p at least.I find it really not fair to compare image quality by saying that the blackmagic can do RAW, and the GH can't. You can't compare RAW 12 bits with not-raw 10 bits.
Some people (like me) even if they have RAW at hand, won't use it because you have less recording time on your media, more storage needed and post production is heavier.
I do documentaries for TV and they just won't accept RAW for their post production workflows because it is just not their standart.
that said, I would compare 10 bits files from both cameras to really judge quality.
from what I've seen so far, BMP4K looks nice, but nothing I couldn't achieve with my GH5s. but you never know how they make their demo movies, and you have to compare scenes with same lens, same lights, ...
Anyway, side by side would be the best way to say in my opinion.