So the obvious questions first:
Autofocus or manual focus?
Tripod or handheld?
Is it only the 50/1.4, or has any other lens done this to you?
A good test would be to set up everything on a tripod, manual focus on live-view, take some test shots at a few apertures, then switch camera bodies, and do exactly the same tests (same iso, shutter speed, etc).
There should in theory be no difference between using the same lens on a different camera body, whether it's FF or crop, except if there's an AF-problem, the mount isn't seated properly (both of which will be fixed by using MF in live-view), or something very weird (like the aperture isn't stopping down to the correct value if the contact is dirty.
Sure, crop-sensors have higher pixel-density, so any value of CA (in mm) will show up as more 'pixels' wide, but that shouldn't be the difference between 'perfect' and 'unusable', it should just be 'slightly more noticeable'.