First of all you have to know that they work on a collegiate system.

Application statistics Cambridge: http://www.cam.ac.uk/admissions/undergraduate/statistics/

Fees Cambridge: http://www.cam.ac.uk/admissions/undergraduate/finance/

Oxford statistics: http://www.admissions.ox.ac.uk/adstats.pdf

Fees Oxford: http://www.admissions.ox.ac.uk/finance/costs/

Many people would say Cambridge- med and Oxford- law. However, even if it’s the other way around, both schools are fantastic. In fact, many league tables have different opinions on which is better for which.

Usually it is first year students who get to stay on campus. If you want the overall, you have to check each individual college in both universities.

Lastly, for Oxbridge VS Ivy League etc., you have to know what you want to do and why and where you intend to work.