Since a smaller sensor captures a smaller portion of the image circle projected by a lens, and since most lenses tend to loose sharpness at any given aperture as you move away from the center, does it mean a legacy full frame lens mounted on a m43 camera will produce an overall sharper image than if it were mounted on a FF camera?
In other words, will the final image be less soft at the edges, since you're cropping them out?
The thing is, a given lens on FF will project a rather different scene on the sensor than the same lens on mFT, so it's a weird comparison to make right from the start. That said, let's consider some situations.
1. FF and mFT sensors with the same pixel size.
In this case, if the photo is taken from the same position with the same settings, and the FF photo is cropped to the same framing as the mFT photo, the two photos will be pretty much identical.
2. FF and mFT sensors with the same pixel count.
Assuming, again, the photos are taken from the same position with the same settings, when the FF photo is cropped to the same framing as the mFT photo, it will be pretty much identical aside from having much lower resolution.
3. FF gets closer to maintain the same framing as mFT.
In this situation, the perspectives will be different, which may be a good thing, a bad thing, or neither here nor there. If the FF photo uses the same relative aperture, it will have half the DOF. If it uses the equivalent relative aperture, the photos will have the same DOF, and the FF photo will have higher resolution if it has at least the same pixel count.
Hope this helps!