In fact, if your direction is not academic but financial engineering, there is not much difference in mathematics between Berkeley and the University of Southern California. If you are mainly academic, I definitely recommend you to go to Berkeley. After all, a high academic ranking helps you to continue your academic application. Speaking of stress, Berkeley is really under great academic pressure.
It happens that my friend is an undergraduate at Berkeley and I am an undergraduate at Southern University. There is a subtle comparison in our communication meeting. The internal competition in Berkeley is much fiercer than that in Southern California, and the GPA deflation is also very serious. I met a few people who couldn't go on studying and dropped out of school. Mathematics at the University of Southern California will definitely be easier. There are not as many students as public universities like Berkeley, and the software and hardware conditions are much better than Berkeley.
Advantages of typical American private schools. I still suggest that you choose schools according to the advantages and disadvantages of public schools and private schools. After all, undergraduate study is an environment and a basic education. I generally recommend that students choose private undergraduate courses, and graduate students only look at majors. The knowledge that undergraduates can learn does not touch the edge of professional ranking at all. Top30 or even Top50 will not have a big gap in the basic courses for undergraduate majors.
Calculus and linear algebra at Berkeley are different from those taught at the University of Southern California. I can say that even the textbooks and outlines are similar. Therefore, when choosing an undergraduate school, students should actually observe whether they like the atmosphere of this school and whether they want to stay in this school for 4 years and then call it their alma mater.
In the end, you have to choose your favorite university, not just because this school has a high professional ranking, and then you will not be happy for 4 years. Choosing an undergraduate school feels like choosing a home. After all, real alumni in the United States generally refer to undergraduate graduates. Only the undergraduate school is your last real alma mater.