Berekely is a top 5 world university, and has been for a long time
Here's the truth, and I don't want to offend anyone
Berkeley is not only equivalent in terms of faculty, and students, it's superior to Cambridge
There's around 30,000 undergrads, and the average student level is very high. The top students though are really elite
We have the Putnam exam in North America, which is a yearly mathematics competition for all undergrad students.
Many IMO Gold medalists from other nations come to the States to study, and our IMO team just won first place this year, so the competition is superior
Berkeley had 14 students in the top 470, which is considered the honor roll. That number is higher than every Ivy except Harvard and Princeton
Quality of your peers is another very important part of your academic life, and the applicant pool for the top American universities is far greater
If you go by research or faculty, Berkeley again is a world leader in literally every department. Superior to Cambridge,in fact. Look at the Leiden rankings which measure research output in an objective manner. Berkeley is above Cambridge in every field, and not by a small margin
Cambridge and Oxford are historically great universities, and are still very good/great for certain subjects, but their trajectories are on the decline