dlee, not sure actually what you mean about Powerhouse. USC has a VERY large student population for a Private. Over 17,000 undergraduates and a similar number of graduate students, all shoe-horned into a pretty small geographic space.
USC is the host for ARTOC, NROTC and AFROTC, so there is a good visible presence on campus. Don't know how many AROTC are there, but NROTC when I checked 18 months ago was about 30. I would guess AROTC would be about 50.
If by Powerhouse you mean well respected, then I don't think you can really answer that. You can ask who won the MacArthur awards each year, but that represents only about 1-2% of schools. You can ask how the cadets of the 270+ Host Battalions performed at LDAC last year, but there are only about 30 schools that had multiple cadets receiving awards at LDAC, with 240 or so sending just one or no cadets receiving the awards.
Another issue is that a Battalion might have a PMS of the Year, or some such Cadre award, but that PMS is likely to be gone from that Battalion by the time you are an MSIII, which is the year a cadet enters Advanced Course and starts to gets mentoring from the PMS. Before that time it is other Cadre who mostly interact with a cadet. Most PMS serve 2-3 years at a school. Now, having a crack civilian HR Administrator at the Battalion is worth gold, but that's another subject.
That is not to say one Battalion is the same as any other. I think absolute Size is important, both positively and negatively, and that it is hugely advantageous to be a student at the Host Battalion vs. commuting from a cross-town affiliated school. However, USC is neither very large nor very small, and is a Host Battalion. So there isn't really much to differentiate it from 100 other medium sized Host Battalions.