I can post pics of my trials if anyone is interested who is switching to another manufacturer... especially you Olympus users!
There are some features that I use regularly on my E-M1 MkII where I'm not sure if other manufacturers offer something similar:
1) Low-light focusing. It's essentially night vision: the camera slows down the refresh rate so that you can still see the scene before you and manually focus.
2) Workable electronic shutter for silent shooting. The sensor readout speed on the E-M1 MkII is 1/60 (one website claims 1/100); the Sony a9 is 1/160, but most other cameras seem to be 1/30 or slower. Slower readout speeds make you more susceptible to weird motion-driven warping in your photos (the jello effect, but captured in a single frame).
3) Close-focusing ability. I'm not talking about macro lenses, but standard lenses. My children are little, and I stick close by them; I've never had to back up to get a photo in focus with my Olympus gear. When I compare the minimum focusing distance on other systems' lenses, it seems like the minimum distance is double.
4) Silent lens operations (autofocus, aperture).
Less critical, but still of importance:
5) A "pro capture"-like feature. This buffers photos around the time that you actually press the shutter, so a single shutter press can result in 18 or 60 photos (if I remember right), with half being from before the shutter press and half being after. Really nice feature for capturing that "perfect moment" (or even just other interesting moments) in action or nature.
6) A lens like the 12-100mm f/4. This one doesn't seem to exist anywhere else - I think Sony has a manifestation of it, and it's not well-regarded optically.
My other system is in the Fuji GFX "medium format" line. It lacks a lot of features compared with the Olympus, and the ergonomic errors Fuji made with the camera body are really incredible. They even have lenses that have external focusing elements, which is something I'd thought was a relic of older or cheaper lens designs. Olympus' build quality is higher, despite being about a fourth of the cost. The sensor is wonderful, but if I blind myself to EXIF data I can't reliably tell which camera I used for which photo, even with pixel-peeping. Even after buying it, I still use my Olympus regularly - and actually, more often than the Fuji. If my wife said I could only keep one, I'd keep the Olympus. A camera is more than just a shell built around a sensor.
I don't think any manufacturer can truly take Olympus' place at this time. Partly for that reason, I'm not going anywhere. I've stopped looking for a second µ4/3 body, but if my E-M1 MkII were to die today, I'd probably buy the E-M1X or E-M1 MkIII. If those weren't available, the Panasonic G9 would likely be a viable option (although autofocus performance would take a bit of a hit).
When it comes to changing lens mounts entirely, the safest bets seem to be either Sony or the L-mount alliance. Sony has a lot of innovation, and as the makers of the sensors that nearly everyone uses I'd imagine that they'd be the last camera company standing, if it ever came to that. But it seems Olympus and Fuji shooters hate Sony colors, and I've heard criticism about their build quality and menu system. Panasonic's S-series of cameras and lenses is the next safest bet, and it sounds like they're the closest to Olympus in build quality... but the S-system gear is big, heavy, and extremely expensive (although Sigma's lenses could dampen some of the price shock).
No great option at this time; hopefully the camera division really will continue onward.