There may be other criteria that plays some role - but AAU membership is PRIMARILY a research ranking. That is really what it measures and rewards. So although i agree that is an important element - many fantastic schools - particularly those with an emphasis on liberal arts and also those without medical schools are virtually automatically eliminated from potential membership in AAU. Before people start throwing out the exceptions, this is generally true but there are exceptions.
For that reason i would disagree that it is a better measure of overall university quality. U.S. News is the universally used common measure for that. Not perfect but the best available option and it is used by virtually all Provosts to measure their University improvements (or lack thereof). Obviously any system that relies on self reporting can be manipulated, but punishment has been pretty harsh for those that are caught - and it is pretty rare.
Those that do not like U.S.NEWS are usually those that have high research but are still pretty poor on student quality (like Texas Tech and Nebraska for example). They always like to talk about AAU, even though it is totally divorced from quality in their case.
Also - no idea why this is still on the football board since it is morphed into an egg head discussion.