"Comparison is the thief of joy," as my mom would say. I know current grad students at Rockefeller and they said that during their interview process, the students that were cocky and came across as if they knew everything were not the ones that wound up getting accepted. Just be yourself and try to explain your science and passion for the program in the best way that you can
It is always good to send thank you emails to the faculty that interviewed you! Try to mention something that you talked about during the interview in the email as a reminder of who you are but also to show that you remembered the conversation.