@Dinoian, After my first term here at UCLA, I honestly didn't feel lost or "just a number", not I don't really care anyways. I think UCLA is what you make of it, it's all up to you. I know some people who hate it here, but I also know most people, including myself, love it. I think if you're the kind of guy that can stay on top of studies and proactively look for your "niche" then you'll do well.
As for prestige, I think the two are equal in the sense that they really can't be compared. They're strongest in their regions, and when you have that UCLA or Rice name in your resume, nobody would really think that "This kid din't go to (insert school here)?", they'll think that "Oh, he went to UCLA/Rice, a reputable and competitive, if not prestigious, school."
For Graduate School I think it's more of the prestige of the department that you'll be in, your grades, test scores, and recommendations as well. For Law though, you just need to have the grades and the test score.