I have a similar story; undergrad at a public state school and grad at a private Ivy. My experience at the Ivy was eye-openi. The loudest [1] Ivy undergrads came from private elementary/high schools and had a very dismissive view of the students who matriculated from public elementary/high schools. Academic breaks were used for luxury travel.
[1] "loudest" in the sense that they made sure that other students knew where they came from.
[1] "loudest" in the sense that they made sure that other students knew where they came from.