There is no University that is more academic and intellectual than the University of Chicago, which has an excellent history in all fields since the day it was founded. This is why UChicago and Cambridge are basically tied for Nobel Prize Winners (ok, Cambridge has one more--88 to 87.)
OK, so you must be British. If you were American, this would be an easy decision. Absolutely no one in America has any interest in going to Oxford or Cambridge for college. (They will go to Oxford for grad school if a Rhodes Scholarship is involved.)
I am not knocking Cambridge but this is a simple truth. I live in California. If you look at one of the top elite prep schools in LA, over the past 4 years they sent dozens or perhaps hundreds of students to UChicago, Stanford, MIT, and the Ivies--and exactly 1 student to Cambridge--in 4 years. Mostly because no one applied there.
An American would always choose UChicago since it has a much better reputation in the U.S. and they don't want to study overseas.
Cambridge doesn’t even exist for Americans; it is simply not on their radar screen.