As an old user of the GX85 (G80 in UK) and a new owner of the Olympus EM10 Mark II these are my thoughts so far. Not a technical view as I haven't had much chance to test the Olympus outside much due to Gales and Storms. Size wise I prefer the GX85 as it fits into my existing bags better, but I much prefer the grip, size of dials and viewfinder of the Oly. With the GX85 I tend to squint with one eye, but with the Oly I can keep both eyes open and still see through the viewfinder. I believe that this is because it protrudes more and is in a central in position.
I nearly always shoot in RAW with the Panny as I don't like the out of camera jpg files, however with the Oly I have found out of camera jpg files to be very good. Jpg files in the Panny don't give much possibility of post developing, but the Oly jpg still allow for quite a bit. Colours I find are more pleasing with the Oly jpg's and don't suffer from being oversharpened.
Initially I have found setting up the Oly to my way of working took a little time, but I seem to have it customised to my liking now. I cannot find any difference with using the 20mm lens on the Oly or the Panny as they both have 5 axis stabilisation in body. ( 20mm lens is not stabilised).
At present I intend to use the Oly with jpegs as they seem to be very good, but will probably revert back to RAW as this is how I have always worked. We shall see. I am mainly a landscape photographer due to living by the sea in a National Park, but also like to do macro, street and urban and I find both cameras fine for this. I rarely do night photography so can't advise on this.