Way back in July, I bought a Panasonic GX85 along with an Olympus E-M5 II with the intention of trying them both out and keeping the one I liked more. As you have read here, that trial was put on hold for a long while, because my initial copy of the GX85 had a bad sensor, and Panasonic, to put it mildly, took its own sweet time to send a replacement.
But now I've had a chance to play with both cameras in different lighting conditions and using the same lenses, and I've made my decision. As of two days ago, the GX85 has been sold, NOT at all because it's a bad camera--in fact it's a sweet little camera--but because I enjoy shooting with the E-M5 a lot more.
There's precious little to choose from here if you're just evaluating image quality. The two cameras, after all, have similar if not identical 16mp sensors, and they both feature effective IBIS. The Panasonic might be just a tad sharper at telephoto distances with a Panasonic lens, because of the new "dual IS" feature. The Olympus renders better (to my taste) JPEG output, but not by a large margin. I almost decided to keep both cameras, the GX85 for use with the Panasonic 100-400mm and 35-100mm (the little, cheap one) lenses, and the E-M5 for everything else. I didn't do that because the whole reason I've switched from Nikon to Micro 4/3 was to cut down on weight and volume of equipment I carry, and also because I already have the wonderfully tiny Panasonic GM5, which makes up in miniaturization for what it lacks in state-of-the-art GX85 features--in good light with fast shutter speeds, I can't really tell the output of the two cameras apart, and the GM5 with the 12-32mm zoom or 20mm prime really does fit in my pocket.
Both the GX85 and E-M5 are somewhat problematic for a photographer with big hands like me, and they both have, for my shooting style, too damned many buttons that are easy to push by mistake. Addition of a grip helps. The thumb grip I installed in the hot shoe of the Panasonic not only provided a solid handhold, it also kept my thumb away from the little buttons on the back of the camera. The Fotodiox grip I put on the E-M5 is a wonder--an absolutely perfect fit that should have come with the camera to begin with, that doesn't lose the tripod mount (which I use mostly for my Black Rapid strap) like the more expensive grip from Olympus. I still needed to change the function of the HDR button on the top of the camera because it's way too easy to hit that one in error than it should be. Luckily, the ponderous Olympus menus (score one for Panasonic's simple, intuitive menus here) do allow you to reassign button functions. I chose focus peaking, but there are lots of better options than Hideous Disney Rendering.
What it really boiled down to was the shooting experience. Between the much better viewfinder, overall precision feel of camera and controls, and always-accessible Super Control Panel, the E-M5 is just more fun to shoot with. And that's how I made my decision.