Well, the 1Dx has only 144 pixels per millimeter, while the 7DII has 244 pixels per millimeter. Given the fact that the same lens on both bodies puts an IDENTICAL size image of a subject on both sensors, the same object gets captured with 70% more pixels in each direction, leading to 'more detail' in the capture by the 7DII. The APS-C image would 'win'. This is the proverbial 'reach advantage' said to exist between APS-C and FF-- depending upon which two bodies you are comparing!
If you put format-appropriate FL on the two cameras, a 100mm lens on the 1Dx and a 60mm lens on the 7DII, the same subject will be 67% larger on the 1Dx sensor.
If the object image were 6mm tall on the 7DII sensor the image would be 10mm tall on the 1Dx sensor. So the same object would be captured with 6mm*244pixels vs 10mm*144pixels, or 1464 pixels tall on the 7DII and 1440 pixels on the 1Dx which is a negligible difference in quality from the standpoint of image resolution of the sensor, and ignoring the optical resolution delivered by the lens. draw
If the two lenses both delivered 100 line-pairs per millimeter of detail resolution to both sensors, the 7DII would be capturing 600 line-pairs of detail across its 6mm tall subject image on sensor, while the 1Dx captures 1000 pine-pairs of detail across its 10mm tall subject image on sensor. The FF image would 'win'.
The above ignores the issue of signal vs. noise content, where one would be superior to the other with regard to freedom from noise at high ISO, or when the image is 'push processed' to bring up details in the shadow areas.