I am a bachelor student in mathematics in Switzerland, and this question has been on my mind for a while.
To begin with, how much does the university you're studying at influence your "mathematical skills"? In my country, the bachelors in mathematics are pretty similar, for ETH and EPFL for example. The true difference is the number of students and the professors who might come from MIT and other top universities. And now, if we compare it to a smaller one, having a ~30 students class for one course with good professors (meaning that they have done great research in their field), isn't a student better prepared thanks to the proximity with the professors, in comparison with a top one having ~400 students? Hence, why should you prefer a better known university over a smaller one?
Surely, when you are doing a Phd you'd want to be near great researchers, but when learning the basis, aren't you better trained in such a smaller university (at least for bachelor)? Or if it is not the case, and you'll be far more better trained in well known university, is your ability to later do research in peril?
On a broader sense : what choice should guide you, when what you want is to contribute as much as possible to mathematics?
Any comments appreciated, feel free to share personal experience, or to speak in a general sense.