Private college vs Public College?

Im wondering about going to either Emory University or University of Georgia. I personally value the quality my education and I have heard that Emory is a better school. But in my opinion facts are facts and wherever you go to school you will get the same education. I like bigger classrooms anyways so I seem to like UGA more and I think Emory is is a too much money. However, I want to be a neurosurgeon and was going to major in Neuroscience. Emory has it and UGA doesn't. Could I still be a good doctor majoring in Biology, Chemistry, or Biochemistry at UGA or Neuroscience at Emory and am I correct that I will get the same quality of education at UGA than at Emory.