For one, I asked you what exactly you meant by "the APS-C lens has to be better than the FF lens"?
I followed that up with a clarifying question asking if you were talking about two different lenses such as one EF-S lens and one EF lens.
Sorry if I was the cause of any additional confusion...
-Yes, to get two images, one taken with APS and one taken with FF appear equally sharp when viewed at equal presentation size in your presentation format of choice, the lens used on the APS camera needs to be sharper, when sharpness is defined by "lines or line-pairs per mm".
-Yes, at least I am talking about two different lenses in the comparison. Why compare an 85mm on FF with an 85mm on APS? they don't "do" the same thing any more. If the shot taken with the FF camera was at a 10 feet target distance, you'd have to back of to 16 feet to get the same framing on APS. And by backing off to 16 feet, you change the perspective of the shot so much that it wouldn't even be the "same shot" any more.
Taking that into account is where the "FF is sharper than APS" starts to make sense....
Using a 135L 2.0 wide open on a 5D3 gives the same field of view, the same short DoF and the same amount of noise as using the 85L 1.2 on a 60D. But the 135 on 5D3 image will be a LOT sharper and more contrasty.
For the same reason, a bog-standard 85/1.8 on FF gives sharper images with the same short DoF as a 50L 1.2 does on APS. And a 50mm vs 35mm F1.4 on APS and so on.