Can you elaborate, please? I mean, if you were to take a hypothetical 25.6 MP FF sensor and use scissors to trim it by a factor of 1.6 in each dimension, you'd end up with a 10 MP APS-C sensor. Using the same lens, there should be no difference how it resolves before and after trimming, right?
P-Mpix isn't a measure of resolution, although resolution is a contributing factor. Resolution ≠ sharpness. A true measure of spatial resolution involves a physical distance. Usual units are line pairs / mm (LP/mm). For a spatially normalized measure in LP/mm, the higher density sensor will outresolve the lower density sensor.
However, that's a per-unit basis - and that's not how we look at images. MTF50, a commonly used measure of sharpness, is reported in line pairs / picture height (LP/PH). In that case, the greater 'height' of a FF sensor means higher values. You can see that on photozone.de - when you compare a lens on FF vs. APS-C, the MTF50 values will be higher for the 5DII tests than the 50D tests, despite the higher pixel density of the 50D. This isn't just a numerical phenomenon - take a look at the TDP comparison of two 18 MP sensors, the 1D X vs. the 7D (same lens, the 200/2L IS at f/4). The 1D X is producing a noticeably sharper image.
P-Mpix isn't exactly measuring sharpness, either. It's basically a measure derived from subjective quality factor (SQF), which simply put is an MTF measurement that's adjusted to match human perception (the psychophysical basis is that humans percieve some spatial frequencies better than others, and viewing distance is relevant to perception of sharpness, too).
That difference you see in TDP's ISO 12233 crops can be measured by SQF, and that's basically what P-Mpix is telling you. For example, the Canon 300mm f/2.8L IS II that delivers 22 P-Mpix on the 5DIII achieves only 14 P-Mpix on the 7D. In fact, the 300mm f/4L IS at $1400 delivers better perceived sharpness on the 5DIII than the $7000 supertele lens on the 7D.
Neuroanatomist, thank you for the reply. I believe I understand your explanation, but I think I am not making myself clear trying to communicate my point.
I agree that sensor size matters if we look at the whole image. In your example, 1D X and 7D have exactly the same number of pixels, but different pixel density. By spreading its pixels over 2.56 times larger area, 1D X is less demanding on the lens and resolves more LP for the same PH.
However, I am not trying to compare the final image in terms of FF vs crop sensors. Instead, I look at the per-unit resolution to show that a good lens should not be the limiting factor for a 22 MP FF sensor. Looking at Photozone.de APS-C tests with different lenses, there is often substantial improvement in LP / PH, going from 8 MP (350D) to 15 MP (50D). 350D with 2304 pixels per 14.8 mm height has vertical pixel density of 156 pixels / mm and 50D has 214 px / mm (3168 / 14.8 ). So, these lenses obviously do not limit the system at 156 px / mm, and can benefit from increasing the sensor density up to at least 214.
Now, 5DIII has 3840 vertical pixels per 24 mm, i.e. 160 px / mm - about the same as 350D. Doesn't that prove that another FF sensor with increased pixel density (more MP) would produce better overall resolution (LP / PH) without being limited by the lens? A FF sensor with the same pixel density as 50D would be 38 MP.
This post from Roger at Lensrentals seems to confirm my speculations. In short, it concludes that Nikon D800E with a good lens (Nikon 24-70 f/2.8 ) out-resolves the 5D III with a great lens (Canon 24-70 f/2.8 Mk II) and that the difference is bigger with the same lens (Tamron 24-70). While P-MPix, being a subjective QF, might not reflect the improvement (thank you for clarifying that), I originally wanted to make a point that a FF camera can benefit from more MP beyond 22 MP, even with the current lenses, contrary to your original claim.
Of course, I understand that these are lab tests and these results may not be relevant in real shooting conditions. Also, they may be partially attributed to removing the AA filter.