At the graduate level it depends to some extent on what you want to study. For what I was studying in Grad school, UC Berkeley is one of the best in the world (in the single digits). It is a very good university overall.
That probably has as much to do with geographic proximity as anything else.
Where I live (mid-Atlantic), many Ivy aspirants would choose Michigan or UVa as “target” alternatives. I’ve never met (or heard of) anyone in my area who applied to Berkeley for undergraduate work. There are too many good, closer alternatives between here and the West Coast.
In undergraduate admissions, HYPSM seem to compete much more with each other than with Berkeley. But you could say the same of almost any other college besides Berkeley. And I’m basing this observation on the cross-admit statistics. I have no idea how many Berkeley applicants don’t even bother to apply to any Ivies or other top privates (just because they actually prefer Berkeley.)
One of the biggest barriers to true undergrad “peer” status is pricing. If Berkeley (and other “public Ivies”) were full-need need-blind colleges for all applicants (or at least for US citizens) then more top students all over the country might choose them over many of the T20 privates.
@tk21769 For OOS students with financial need, all the UCs have been at a disadvantage given that their financial aid did not cover the OOS supplement. It’s even worse now that they cannot make any grants to OOS students. They’ve essentially limited their base to those students with money.
Of course if you ask faculty about peer institutions, Berkeley is invariably mentioned.