A lot of the information on this thread is out of date. (And last year's admissions were truly crazy because of COVID.)
So, here's the deal, for the Ivies you need exemplary grades and test scores AND you need a hook. The number of AP classes only matters in comparison to the other kids at the same school. If the average number of APs taken at a school is three, then you need six. You don't need 10. But if the average is higher, then you do. Cornell is the one exception to this--it's big, out in the boonies, and low-enough ranked that it actually does have to compete with non-Ivies for its students.
The hooks are being a legacy, an athletic recruit, some sort of glossy extracurricular, rich parents willing to donate or being an URM. (Underrepresented minority--i.e. not Asian.)
Since 2008, rich kids whose parents can pay full tuition have a distinct advantage. Kids who fall just under the cut-off also have an easier time--the schools like to pay out as little as possible while keeping up the illusion of having lots of kids on scholarship. It is very, very hard to get a full scholarship.
The schools say that being a legacy doesn't make that big a difference, but if you're hitting the grades/test/class-ranking metrics, that little thing will make all the difference.
Duke, Northwestern, Johns Hopkins tend to hang together in the rankings--near the bottom of the top 10, but always in the top 20. Rice, Vanderbilt, USC, Emory, Georgetown are below them--reliably in the top 30. NYU, Berkeley, UCLA as well. Cornell, Brown and Dartmouth tend to place between those two groups. Penn is hanging on, but I expect there will be a shock switch with, say, Duke, one year.
Stanford and MIT are a cut above and vie with Harvard, Yale and Princeton for top dog status. University of Chicago and Columbia maneuver their way in there on occasion, but Chicago just doesn't have the same appeal. And, yeah, Brown is known for taking dumb, rich kids and making it easy for them to get through. (Sounds way more fun, though, than, say, Columbia.)
That said, the elite non-Ivies probably have the better students just because there's less of an issue with legacies and athletic recruits, at least for UofC and Johns Hopkins. Duke and Northwestern do do the legacy/sports thing. Northwestern tells legacies to do early decision--admit rates for early decision are 20 percent, for regular decision it's around 5 percent. Athletic recruits are also pushed to do early decision.
It is *much, much* easier to get into any of these schools as an URM, which, ironically, ends up reinforcing stereotypes. Yeah, the Asian kids are at the top of their classes because it's so fucking hard to get into these schools as an Asian kid. The dumb jock stuff continues because, yeah, as an athletic recruit, you don't need the same grades and scores as an unhooked kid from the burbs. Meanwhile rich kids, who don't have to worry about financial aid, applied early decision, when it's easier to get in and, yeah, compared to the little unhooked grinds who got in regular decision, they come off as pretty lazy. They literally didn't work as hard to get there and they know it.
As for the UCs--The top UCs are heavily Asian--Berkeley, UCLA, UCSD, Irvine (the latter two lack the prestige of the first two, but are strong in STEM) The bottom UCs (Merced, RIverside, Santa Cruz) are heavily Latino. White kids dominate the middle--Davis, Santa Barbara. The UCs end up with the Asian kids with excellent grades and scores who don't have enough of a hook for the Ivies and other private elites. Since the savings are substantial for in-state residents who don't qualify for big-time aid, people are okay with it. (The real bitterness comes from the kids who are good students, but who still don't make the cut for any UC other than Merced. Seriously, if you're a good enough student to get into UCLA, you're good enough to get into a higher-ranked private (at least if you're not Asian).