Let's say I shoot a FF Nikon D5 (21 mpx) with a 400mm, vs a APS-C D500 (21 mpx) with the same lens. The D500 would have an effective range of 600mm (1.5x multiple).
If I crop the D5 (FF) image to size same as the APS-C so the magnification is the same, would the D5 have the same image quality as the APS-C image?
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assuming (and these assumptions are key) that the scene is shot from the same position with the same lens at the same focal length, aperture, and exposure time, and also assuming that the sensors have the same pixel count and record the same proportion of light falling on them, and the FF photo is cropped to the same framing as the APS-C photo, then, yes, the APS-C photo will have "higher IQ" because all else is equal and it puts more pixels on the subject.
However, the above presumes the desired photo is taken. If, for example, one camera has faster and/or more accurate AF than the other, then even a small difference in focus accuracy may result in either losing the IQ advantage or extending the IQ advantage. If one camera has a higher frame rate than the other and thus captures a better photo than the other, then this better capture may trump any IQ advantage the other camera has. Etc., etc., etc..