It’s a lot like grad school. The PhD program I attended is top 15. There are less than 20 total graduate students and only 3-4 new students get in each year. It’s really selective. Once you’re in though, you have to go out of your way to fail.
I know some people who went to undergrad at Harvard and Yale. They said they don’t think it was much harder than a top level state university. The people who went to MIT and Stanford said school was pretty challenging though.