I transferred from a state school to a top school and the difference was night and day. There was suddenly a much larger variety of advanced courses to choose from. There were faculty who were experts in more esoteric niches. Coursework was harder, expectations higher. And, perhaps most importantly, my new peers were incredibly accomplished, and I could learn as much from them as I could the professors.

At the state school, if you were really, really good at your coursework or were taking advanced classes earlier than normal, you stood out so much that there was actually a sense of isolation. It made me feel fairly uncomfortable in a few cases, which is one of the things that led me to transfer away.