I think UCLA might be a better premed education, because of the research opportunities as well as the fact that based on the attitudes of nearly everyone I've met associated with the UC system, I wouldn't be surprised if they greatly favor their own (I'm assuming as a CA resident that you'll be applying to all the UCs).
But, I left the UC system (UCI) after two years due to a couple or years due to a couple of things -- mainly the social atmosphere and competitiveness of actually getting the great opportunities. I was in the honors program so I was supposedly promised funding for research, but I was never given any guidance on how to actually do it, I wouldn't have known how to write a proposal to actually get my funding. To get actual research experience if you're not in the honors program and can do your own (at least as a psych and social behavior major) you have to compete with a bunch of other undergrads to be some grad student's bitch. And socially, I couldn't really identify with most of the people on campus. My experience with UCI as well as people from UCSD (I live in SD so I get to know them) is that there's a disgusting amount of intellectual snobbery and competitiveness. I could mostly escape it hanging out with people from my own major (psychology and social behavior) but it's at its worst in premed students. I had a study group in a cafe once and a girl came up to us, asked what major we were, and said it's really nice how we can study together and she wished she could do something like that but she's a bio major and they're all too competitive to get along.
In fact, I'm not sure that if I were to get into a UC med school, I'd even go, even though I'm a CA resident so they're definitely my cheapest option. When I think about being completely surrounded by UC premeds...I think I'd rather pay more to go to a lower rank school just to be around more laid back people.
So, there's definitely something to be said for private school. I transferred to one, despite being on full scholarship at UCI. You won't have the opportunity to do assist with cutting edge research, but they'll create opportunities for anyone who wants to do their own. You don't have to compete, you just have to ask. Because there aren't limited resources, everyone can get along and want each other to succeed. You'll have more intensive advising to help you along. There are no grad students that we have to suck up to or compete with for professors' attention. The school is really invested in getting everyone into grad, law, or med school. And despite the fact that this is the best school in its state and UCI definitely isn't, there's way less intellectual snobbery. It was definitely the right decision for me, ESPECIALLY since, as a senior, I've decided I want to use the premed resources. The fine print is that I don't actually know anything about Chapman so I can't promise any of this would hold true there. But I bet it would at most decent private schools, especially liberal arts colleges without grad programs.
The bottom line I guess is that it's a matter of personality. Many people love the UC system and I'm grateful as a Californian that it provides us with a world-class education at a very low cost, not many states have that. But if you're not a competitive type or an overachiever type it might not be for you.