An American friend once explained to me what he saw as the differences between university admissions in the UK and the US:
UK PhD: You apply to a program typically offering between a few and a few dozen places each year.
US PhD: Similar
Cambridge first degree: Similar
Harvard undergraduate: You apply to the university for one of 1,800 places each year.
UK PhD: You commit yourself to studying a specific subject before entry. It is very uncommon to change subjects after entry.
US PhD: Similar
Cambridge first degree: Similar
Harvard undergraduate: You typically don't decide your major subject until the end of the first year. Even after that it is not uncommon for students to change subjects provided they are willing to study for an extra year.
UK PhD: Admissions decisions are made by the professors who will be supervising the students.
US PhD: Similar
Cambridge first degree: Similar
Harvard undergraduate: Admissions decisions are made by a central department of administrators.
UK PhD: The admissions tutors would regard it as a great success if, after 20 years, all of the students they admitted have become tenured professors in their field.
US PhD: Similar
Cambridge first degree: Similar
Harvard undergraduate: The admissions committee would regard it as a complete disaster if, after 20 years, all of the students they admitted have become tenured professors in their field.
The Harvard admissions committee would like to see some future academics amongst their students, but they would like to see more future politicians, senior judges, CEOs, and other movers and shakers.
AFAIK, @cupcake222 is correct that Oxbridge admissions tutors focus on future academics to the near exclusion of everything else.