Enrollment at UCB is 37k, which only puts it slightly above Harvard (21k), Columbia (22k), Cornell (20k), and UPENN (20k).

Also, UCB outranks most of the ivyleague in the sciences, engineering and computer science on most measures --

http://www.topuniversities.com/university-rankings/world-uni...

http://www.shanghairanking.com/FieldSCI2015.html

http://www.usnews.com/education/best-global-universities/ran...

Berkeley is hard to cluster... the undergrad population has a much more diverse demographic profile (hugely more first-generation college students & more nonwhite students). I'd say the students have more raw talent, but generally less economic and cultural capital than typical students at top-tier private universities. The faculty is Ivy-class (though larger!) but the university itself suffers from periodic shortfalls in the state budget.