I would recommend OP attend the cheaper state program.
A bit about my educational background: I attended Stanford out of high school on a military scholarship. Although there were a lot of classes where grade inflation was rampant, most bottle-neck classes for large majors were pretty competitive (~top 15% get A's, next 20% get A-'s), particularly pre-med/dental classes (although I never met a single pre-dental student in my class at college). It may seem to some that a class where more than a third of the students get some form of an A is not that tough, but when the class is filled with really smart, driven people, you have to work hard for that A-. Anyway, I felt like I worked pretty hard but graduated with a 3.7 average. I had a good number of friends that had been valedictorians with 1500+ SAT scores drop out of the pre-med curriculum because they kept getting B's in the pre-reqs. Paradoxically, the algebra-based physics had a reputation for being more difficult than the calculus-based physics because the former was flooded with pre-meds while the latter was filled with less GPA-conscious engineers.
After about five years in the military, I decided to go to dental school. To fulfill the prereqs I had not completed in college, I did an informal post-bacc at Oregon State. OSU was a great experience for me and very different from Stanford. It was much easier; I didn't really feel like I had to work to get an A so I just focused on learning as much as I could. The professors were really great and committed to student learning. That is not to say that Stanford's professors were bad, I just didn't find them to be any better at teaching at an undergraduate level than the OSU professors. Just because a professor has written a bunch of highly cited articles on a highly specialized niche in their field does not mean they possess great teaching abilities. Some do, and some don't.
This also made getting strong letters of recommendation easier. I stood out a lot more from my peers at OSU than at Stanford. And they don't teach some sort of secret biochem at Stanford that public schools don't have access to, it's all the same material. However, you should realize that barely getting an A at a state school does not mean you have a sufficient understanding of the material. Learn as much as you can, not just what is required for an A.
The one thing I really think was valuable about my college experience was the people I met. My friends from college are some of the most intelligent, successful, and driven people I have ever met. However, I don't think rubbing shoulders with the soon to be rich and famous is worth $200K in debt. I was on a military scholarship so I didn't really care, but I would have chosen differently if I were paying.
In the end, I got a 4.0 in the pre-reqs, got into my first choice school (Harvard), and am really glad I did my pre-reqs at a state school and not a top-tier private school. I recently talked to a fellow non-trad in the medical class who graduated from Yale and then later went to a state school for pre-reqs about our experiences. We both couldn't believe how easy it was to get A's after leaving the hyper-competitive environments where we went to college.
In sum, state schools can give you an excellent education in a less competitive environment. The professors are highly qualified because getting tenure anywhere is very difficult. Any tenured or tenure-track professor will be more than competent in their field (although as an educator, that is hit or miss...). Many state colleges offer honors programs that allow you to be surrounded by similarly driven students in order to provide the sort of intellectual environment normally found in more selective private schools.
