IMO, in terms of options and operability, the OMD EM10MK3 isn't anywhere in the league of the GH series. However, the Oly is smaller, lighter and has it's own filmic look that I miss in the Lumix cameras. It's a "fun" camera but not as "serious" as the GH series. The viewfinder dynamic range isn't good and it doesn't have any metering in manual video mode, however the viewfinder is really quite good for judging correct exposure.
Generally, I've avoided 1080p in any form and the tele convert function as I've always been left disappointed. Just love the full 4K image though, especially with sharpness turned "all the way down" -2.
I'm picking up this camera more lately for it's more sensible size and lovely image. This camera paired with the Oly 9mm lens cap is pocketable. For me, this is the GH2 of 2018. One reason I'm glad Anderw mentioned it. It's small, inconspicuous and with it's beautiful tiny fast primes, a Q-ship in keeping with the m43 philosophy.