How do you pick a school?

IRL, chances are when you as parents of elite school kids are asked to share your insights are for a scenario like this: My son is deciding between Stanford and our respectable state flagship. His Academic interests are wide and
we don’t know what path he will end up with. He feels comfortable in state flagship but a little intimidated by Stanford because he never attended a private school. The tangibles at both are comparable in terms of meeting his needs. Obviously, Stanford is a much more prestigious college than our state flagship, but we do need to pay about 8000 more to attend Stanford because state will be a free ride, but 8000 is within our budget. What would you say? Would you say oh a prestigious private school is not going to help you in any way if you feel your son can get the education he needs (typically any state flagships can fulfill most students’ need) in your state flagship?