I think everyone would agree that the 1Dx has better IQ than the 7D. I haven't actually looked at any 1Dx photos, but I think that is a safe assumption. So this sort of makes the argument for crop body counter-intuitive. Overall, the 1D wins. But, if you pick any section of a 1Dx image that is the same size as a 7D image, then the 7D image is better than just that section.
The answer is still the same:
"However, image quality is not only resolution: those less pixels will have much less noise than 7D pixels, so from that point of view IQ will be still better."
What you speak of is
number of pixels (and
resolution, up to a certain point), not overall
image quality. The larger physical pixels of 1Dx give much less noise than 7D. This is really crucial for IQ, and the main reason why everyone will agree that 1Dx has better IQ than the 7D. If you look at dark areas, with 7D, even with more pixels, you will see noise, while with 1Dx not. This is IQ (at least one component). But if you speak of pure pixel count yes, the same scene shot with the same lens and then cropped on a 1Dx will have less pixels than on 7D. And on 7D you will see some smaller details (depending also on lens), but just because you used 1Dx in the wrong way.
A nature photographer would choose a crop body for the same reason: more reach at cost of some noise, instead of buying a longer and more expensive lens on a FF.
By the way, everyone would compare the same exact scene, to evaluate quality: so, for example, taking it with a 50mm on 7D and 80mm on 1dx, or walking closer with 1dx to have the same frame.