Top 50 private colleges will cost more than your IS public universities unless a student qualifies for financial aid and merit. Plenty of non-top 50 privates do offer great merit money.
We do not qualify for financial aid, so for us, private schools and OOS publics are much more expensive than our in-state public schools, even with merit.
Private universities will offer a more intimate campus feel, smaller class sizes, more individualized advising, and probably a more diverse geographic mix of students. There may be great alumni networks and great research opportunities, depending on the major.