I did the big, state school undergrad and went to a private grad school. There is no doubt in my mind that the undergrads at the private school, as a group, are smarter, more motivated, more driven, and have more concrete goals than did the students at my undergrad. And that fosters an environment where pursuing excellence is the norm. The state school didn’t have that. It had other, non-academic advantages, and the graduate schools there were excellent, but the undergraduate education, frankly, sucked. And this is reputed to be a top state school.
As to money: talk to the financial aid people. Private schools are more flexible than public, especially if the school is rich. If the offer they’ve made isn’t enough, ask for more (this can actually work; my fiancee was able to go to a top, top private undergrad only because she called them and said, “I can’t afford to come with what you’ve offered me”. They upped the offer (substantially), and off she went.)