I get where you are going but AAU is absolutely important as it demonstrates a university is maintaining set standards of innovation and research which is obviously important. Couple that with R1, which most AAU are, and it's absolutely reflecting quality drivers in education as research, innovation, and leading practices in higher education drives the pursuit to quality, research dollars for more, advances in education/knowledge.
this is not the hill you want to die on
I know Brandeis well and I'll say that PSU is better. Brandeis is a good school but PSU offers more and has more referenced professors, patents, etc etc....you know, all the things a AAU/r1 wants
As for Sarah, not even sure why they are in a discussion here as they are not a peer institution as RU blows them away. Hell, Sarah's best school doesn't even Garner discussion in communications circles any longer.