I go to a state school instead of a private. And as student loans become more of a building reality waiting for me at the end, I am more and more grateful that I am paying less for med school. Of course, there are possible trade-off's. Is the quality of education different? Will the private help put you in position for a great residency and a better-paying career, thus negating the undesired increase in tuition and loans? Or will it simply help you to become a better physician? For both questions, probably not, but I can't answer that for sure.
When I was considering schools, I did have some input from some good doctor friends of my family. One is part of selecting residents for Orthopedic Surgery, a highly competitive specialty. They all told me that the name of the school didn't matter. However, board scores and grades do matter. Now we're back to "will the private school get me better board scores?" Again, probably not, but I can't really answer that.
I think you have to pick the place where you think you will be happiest (in day-to-day living), where you'll be most able to enjoy your education. That means considering the curriculum, the atmosphere, and the location. On the curriculum, I think people have covered that pretty well. As far as atmosphere, is it a congenial, helpful atmosphere? Or is it ultra-competitive? And the location can be huge. I'm in my hometown. My mom brings me food every now and then. I see my good friends from outside of medschool. I know where to go when I have car trouble, when I want to go for a run, or when I want to get a beer.
Complex decision. The good news is, you're going to be a doctor, no matter where you go. If you're excited about it, and try to focus on becoming a good doc, then I think you'll be fine.