oxbridge is completely different to the Ivues in terms of selection
This. I believe that a large majority of students currently at Oxbridge wouldn't have got places in the Ivies, and a large majority of students currently at the Ivies wouldn't have got places at Oxbridge, because they select for very different things.
At Oxbridge, the college tutors who will be teaching the students have very significant input in admissions to their courses. IME, they try to admit students who have already demonstrated deep interest in their specific subjects, have prior achievement in the subjects, and, quite frankly, who think like them, because these are the students who will be easier for those admissions tutors to teach.
At the Ivies, admissions is centralized and faculty have little to no input because students are admitted to a 'liberal arts' course and are rarely required to choose a major until their sophomore (second) year. The university admissions committees will require a minimum level of academics but, once that standard is met, they look for other indicators that the students can achieve in areas which are not necessarily academic.
To illustrate, there's a joke at (American) law schools:
- 'A' students become (law) professors
- 'B' students become judges
- 'C' students become... partners (at law firms)
Whilst the top American universities don't mind producing (a few) professors, their main focus is producing judges and partners and their equivalents outside the legal field, and they select students whom they think can develop into those positions. Oxbridge, OTOH, selects much more for students whom they think can become professors. And these will usually not be the same students.