What we can se in the images is that the sensor on the left can transfer more contrast at each cycles/mm. For instance at 40 lp/mm it would transfer about 58% on the APS-C camera while on the full frame it would transfer around 50%. But, because the sensor is smaller, the relevant comparison is to compare 40 lp/mm on FF with 60 lp/mm on the cropped frame. So here we see that the cropped sensor would transfer about 36% contrast at 60 lp/mm to compare 50% contrast at 40 lp/mm on the full frame. So, using the same lens the full frame camera has a significant advantage in sharpness.

Now, the upper dotted line shows the diffraction limit. An optically perfect lens would have MTF like diffraction limit. on APS-C such a lens would reach around 75% MTF. It is thus theoretically possible to compensate for the format size by building a better lens, in practice that would be very difficult.

The images below demonstrate this difference:

With no sharpening (full frame to left and crop frame to the right):

Or properly sharpened (full frame to the left, crop frame to the right)

Sharpening has a major inpact on digital images. I have not looked into this, at least for now.

Real world MTF comparison based on test images from Imaging Resource:

The image samples above were made using different small format Sony cameras, using essentially the same lens. Below is an MTF based comparison  of the Pentax 645D and the Nikon D800E. This NTF curves are based on test image shot at Imaging Resource. In this case the Pentax 645D was tested with it's standard lens, while the Sigma 70/2.8 Macro was used on the D800E.

Carefully comparing the MTF curves below I would say that the Pentax 645D does have a very small advantage, but the difference is more like an Imprial Quibble (that is small enough not to be significant).