This may not be an apples to apples comparison as many will undoubtedly point out, but I think the analogy can help explain some of what you are seeing. I'm ignoring IS for this discussion.
To freeze motion, shutter speeds must be higher for the smaller pixels found in the APS-C or high-res full frame sensors. I've always used a minimun shutter speed of 1/focal length on FF and 1/2*focal length on APS. But it was really about density, not sensor size. Astrophotography helped me understand why higher shutter speeds are necessary on dense sensors to avoid star trails or blurry images. This table shows maximum shutter duration for various bodies with a 100mm lens attached. The required shutter speed varies based on the density (pixel size) determined by sensor size and MP,
https://www.lonelyspeck.com/advanced-astrophotography-shutter-time-calculator/comment-page-3/. I set the tolerance to 11 pixels to show a better range. To get a 1 pixel tolerance simply divide the shutter time by 11.
sensor | MP | lens | tolerance | shutter (seconds) |
1DXII FF | 20 | 100 | 11 | 6.2 |
7DII APS | 20 | 100 | 11 | 3.9 |
5Ds FF | 50 | 100 | 11 | 3.9 |
Rs FF | 80 | 100 | 11 | 3.1 |
M6II APS-C | 32 | 100 | 11 | 3.1 |
Ra FF | 30 | 100 | 11 | 5.1 |
Whenever there is movement (whether the subject or me), a similar thing occurs - astrophotography or not. I have the 1DXII and M6II and never use the same settings - even when shooting side by side. On the M6II, I've modified the auto minimum shutter speed under ISO speed settings to +1 which effectively halves the shutter speed and doubles the ISO when I'm in Av. In M mode, I compensate with aperture or ISO. For me, post processing can help with noise without downsampling, blur not so much.
When I was looking at the 5Ds I figured I would need to adjust shutter speed by 2/3 of a stop, roughly the same as shooting with a 7DII. I'm now planning to purchase the Rs, knowing that I might need to shoot at half the shutter speed to achieve equivalent effect.