Re Panasonic lens on Olympus...There are a couple of things. One is what Wapiti mentions above, that the Panasonic lens on an Olympus body is more prone to flare, can exhibit the purple blob issue and is more prone to chromatic aberrations. The other is that Olympus and Panasonic seem to be diverging a bit on things like stabilization and the Olympus E-M1 ii offers a feature called pro-capture that will not work with Panasonic lenses. That feature may be of no importance to you. I intend to try the Panasonic 8-18 when it comes out knowing that it won't work for pro-capture.
I have no idea how significant distortion of 7.2% vs 5.2% may be, as viewed in an image, so those numbers don't mean a lot to me. I also simply expect there to be some distortion in such a wide lens. If the one article I cited earlier is correct that the Oly is actually much closer to a 6mm at the wide end, then that, too, would likely explain greater distortion at its widest point than the narrower Panasonic. As far as I know, lenses are no longer designed to correct for distortion themselves. Manufacturers rely on in-camera software. I shoot RAW so I don't get the benefit of that, although you can correct for distortion in photoshop and lightroom.
When we are talking about distortion with these lenses, we are talking primarily about the ability of a lens to keep a straight line looking straight. When I shoot underwater, there are few straight lines and one of my favorite underwater lenses is the 8mm fisheye, for which straight lines simply don't exist. So, I don't care a lot about distortion as much as vignetting and sharpness (to a point). Of course, if what you shoot requires minimal distortion, or if it simply matters to you for other reasons, that is fine. Generally, I doubt anyone could identify which lens was used on any given image.