Well, in terms of branding, I believe it is not true that all universities from US are well known comparing to their peers in Europe. Choosing an offer also depends where you are going to build your career. However, I have seen young professors with PhD from EPFL and Zurich here in Canada. They are both excellent universities with global names. At the end of the day, it is your performance in PhD that matters most for perusing academia not the name of the university (take a look at faculties' profiles in any university that you want and see where they graduated from: you may get surprised).
If I was in your shoes, I definitely choose EPFL rather than UCSD and UTA.