I personally think the education level is about the same, my experience is UK but having compared the courses and content I studied to that of Cambridge/Oxford syllabus I feel like what I was taught was comparable. (I think this may be different if you go to a really really low calibre school, but I'm guessing most teach the same at undergraduate level. After all these really are the basics, which every lecturer knows inside out, so you don't need some famous physicist teaching you E&M, although it would be enjoyable!)
However despite your education being the same, it would be naive to think going to a brand name school doesn't have advantages. You will find this out if you ever apply to graduate school, having the opportunity to do undergrad research under a well known advisor in the field you intend to continue you, and getting him as a referee, cannot be overestimated.
Also in industry if you choose to take that route instead, with all other things equal (GPA etc) the employer is probably going to choose the brand with the prestige and weight behind it.
It's hard to know what you want to do upon graduation, but if it is research then I would advise you to go to a university that has at least some people working in a field you are interested in, so you can get some research under them and have them as referees. I went to a school were no one did string theory, as a result I have done projects and research in other things, not stringy, yet I want to do stringy stuff for my PhD and am finding it v difficult to get a place. No way I would have known this before I started my degree though, since I had no idea what I wanted to do, so it is tricky.