I'm not in admissions, but I speak with admissions people from time to time. My view, which is certainly not the last word on this subject, is that the school makes a difference, but only in how grades are interpreted. That is to say that a 3.8 from a Yale or Columbia will be read differently from a 3.8 from Oklahoma State (with no offense intended towards Oklahoma State). I don't think, however, that admissions offices split hairs on this point. In other words, while it routinely is acknowledged that some schools are better and more difficult than others, such a calculation cannot be made consistently across all undergraduate schools and majors, which themselves vary in terms of difficulty and relevance.
My advice, then, becomes similar to my advice for choosing law schools. If the schools are very different, then choose the best one. Between schools that are relatively closely ranked, however, then choose the one that best meets your particular needs. That's because the rankings are generally, but not specifically, accurate, and because they include only a limited amount of information. For an undergraduate school, you have a much broader range of choice, but there are limits.
I'm an East Coast person, so I can't comment on the UC schools. Still, my impression is that the particular school matters most when comparing like grades between unlike schools, or when the competition for law school is particularly tight at approximately the GPA/LSAT point at which you fall. Excel at your school and you stand a better chance of avoiding the issue of your particular school choice.
Either of those majors would be fine. Choose your major, though, according to your own interests and not by trying to look a certain way to law school admissions. Lawyers come from a very wide range of undergraduate majors. I've been told more than once by admissions people that *music* majors are the most likely to excel in law school! In any law school, though, you would see almost every possible major represented. Do what you love and make sure you get top grades for the schools you mentioned.