I really hate the word
"best" in such contexts. It's meaningless and juvenile. And it's not like the university you attend is going to make or break your career.
There are, of course, better schools. MIT, IIT, Berkley. Cambridge. I want to say Singapore, but I'd have to check.
Closer to home, I was pretty impressed with my experiences with the University of Central Florida, though they're not world-famous I don't think.
Once again, with "best", I don't prefer Computer Science or Software Engineering. Usually my job title is "Software Engineer", often my duties are Computer Science. If you have to formally stick one or the other to your name and reputation, it's a good idea to do some homework. Decide where you want to be working and what would make you the best fit there.
And, of course, if you're planning on a career in the US, allow for the transience of modern-day employment and target the sector you want to work in as opposed to simply aiming towards a single company.