we will try to do this. I am biased. I am a University of Chicago alumnus, and I am a Lutheran who went to a Catholic high school. These things color my thoughts, so take them with a grain of salt.
In the of all, the University of Chicago is the most selective of the listed universities, and the most prestigious. At least if we focus on people who actually know something about higher education. People whose knowledge comes primarily from college football might not know about the University of Chicago.
Chicago is also the most demanding academically. There really is no university in the country that has higher standards.
To credibly claim to be comparable, most cannot. I would not consider any of the others to be comparable, except for Northwestern’s honors program, if that’s still a thing.
This is the University of Chicago is not, however, especially competitive academically.
There is no class rank, and the only classes that have a hard curve are the ones aimed at pre-meds, who need to be made to suffer so their ranks can be culled. Otherwise, while the academics are demanding, it’s very much in the spirit of collaboration. The school is stuffed with people who are very academically inclined, much moreso than at the Ivies, as one example.
But, the University of Chicago is not for everybody. You should only consider going there if you love the idea of the Common Core. It’s the central part of the undergraduate experience, and there’s no way to hide from the expectations. You have to be an all-rounder academically to an extent that most schools won’t require.
This is especially true for the STEM/quantitative types. There’s a bit of leeway for the humanities types to dial back the difficulty in the Core STEM classes. There is no equivalent for the Core humanities classes. You have to be able to read difficult books and write essays that deal with questions beyond what was covered in class, with minimal assistance with learning to write well. Embrace this, or go elsewhere.
As far as the other schools go, I’d say they’re broadly comparable, with an edge to Northwestern. Northwestern has been seen as a very selective/elite school for longer than the others. I do happen to think that the reputations of Georgetown and Notre Dame have historically been inflated by Catholics who put undeserved value on the fact that these are Catholic institutions. I think of one classmate who I highly respected who could have been at least as competitive an applicant to Chicago as I was. His dad decided that if he’s paying for private school, it had to be a Catholic one. He went to Notre Dame because it was the best of the available options.