I have both the Olympus EM1X and the Panasonic G9 so can give you my thoughts.
The EM1X is built like a tank. Mines taken a tumble from my camera bag directly onto a concrete path from about 5 feet and just bounced (although I wouldn't recommend you try this at home kids). The G9 is also well built but not to quite the same nuclear attack levels of the EM1X. Obviously the biggest difference is that you can detach the optional battery grip from the G9 that you can't do with the EM1X, but the latter has surely got to be one of the most comfortable cameras I've ever held, and doesn't seem to weigh as much or is as big as the images would suggest. image stabilization is superb on both and I don't really notice much difference. One note though is if you plan on using Olympus Pro Lenses (e.g. 300mm F4 Pro) on the G9, then you don't' get the benefit of dual sync IS (just like you don't if you use IS Panasonic lenses on the Olympus), but in reality, I've not actually seen a massive difference either way, and they both still work great.
AF wise, I'd probably give the nod to the Olympus, as the DFD system used in the Panasonic whilst good, has an annoying shimmering effect as the AF system shimmy's for focus. It works, bt just doesn't look very pretty. Bear in mind though that the Olympus has the AI tracking modes (which really work quite well, and the aircraft setting actually manages to pick up birds), but the Panasonic recently added proper Animal AF modes and it does work really well.
I wouldn't worry about the menus on both, especially the Olympus as though whilst they might be a bit daunting at first, they are actually quite logical if not as simple as the Panny ones. Both cameras offer a "my menu" area anyway where you can store frequently used items.
Image quality is pretty much a wash between them both so that wouldn't' really be a decision factor, but the Olympus of course has the added benefits of twin High Res modes (both 80mp Tripod mode and 50mp Hand held modes), whereas the G9 only has (a very good) tripod mode with a similar 80 mp image. The EM1X also adds Live, time, Live bulb, Pre-Capture (better implemented that the G9 version), tilt shift function, in camera focus stacking (which again works brilliantly).
Video wise, as good as the files off the EM1X are (max of 4K 30p or C4K 30P), the G9 (with the latest firmware) blows the Olympus out of the water with 4K 60, and the recently added 10 bit 4:2:2 modes and much more in the way of bitrates, file types, and slow motion modes. Also the EVF of the G9 is huge and much more detailed and contrasty than the one in the EM1X.
To be honest I don't think you can go wrong with either, but bear in mind that as of today, a new G9 is only £839 (source - camera price buster) and the EM1X is over double the price at over £2k, so that could well be a deciding factor. To be honest I use both and they are a good pair for each other, but if i had to choose one....hmm difficult.....it would have to be the G9...no the EM1X......oh buggar.....