With ultra-wide lenses, we expect falloff to be a problem. The Olympus and Panasonic lenses both have significant falloff – darkening away from the center of the frame. It's hard to say that one's better than the other in this respect, even though their characteristics aren't all that similar. The Panasonic has darker falloff, but it's more symmetrical. At some apertures, the Olympus lens's darkest points are along the sides of the frame, rather than the corners, and the right side of the frame is consistently darker than the left. It's also notable that both lenses fall off more in the bottom half of the frame than the top.
Fixing each lens's problems in post-processing will present challenges. In either case, the user will lighten the dark areas, and as the areas get lighter, they'll get noisier. The noise issue will be worse with images from the Panasonic, because they'll need more lightening. Automatic software solutions typically use a radial gradient because on many lenses, falloff is nearly circular. A radial gradient won't match either of these lenses' falloff pattern very well. It will be a worse match for the Olympus than the Panasonic.