Sharpness, distortion, displaying images on screen and/or printing them, print sizes... and you could add vignetting, color aberrations and micro-contrast to the list, plus you could want to compare image edges quality rather than image center quality: the edges of a shot often end in the central part of the resulting pano!
Not a stupid question, just a so difficult one that every answer looks more or less stupid from some point of view. For film cameras, people ended in finding some agreement about lens test procedures (FTM, etc) so that the best possible image could be defined as the image the best possible lens would produce on the best possible film: for digital such agreement don't exist yet.
Standard image targets for panoramas are yet to be defined and above all there is no standard stitcher. The different stitchers have many settings which impact the result (like blender options) so that as far I know no image quality comparison was ever published.
Questions like "when shooting 360° x 180° panoramas, is image quality lower using a full frame fisheye rather than a very wide planar lens of identical focal length " (ex.: Nikkor 10.5 mm fisheye / Sigma 10-20 mm planar zoom) are only answered by guessing.
I believe the most common way to select panorama equipment is to watch panoramas and when you find some which really please you and know of the camera, lens, etc, then say "if he can do that I certainly will, too."
I recently changed my photo bag contents and now have to work hard to learn how to use it and must compare results I get from the many possible settings: http://slash72.club.fr/gurl/360x180/size_vs_quality.htm