It's not true that Cambridge is better than Oxford ... It really depends what you want to study; even within a specific discipline there are notable differences (i.e. take Philosophy: Cambridge is great for Wittgenstein and Oxford is amazing for Legal Philosophy/Jurisprudence).
For politics, ir and social sciences in general Oxford has a better reputation overall. On the other hand, natural sciences and maths Cambridge is ahead.
Plus, an Oxbridge education is something unique that you cannot live anywhere else in the world. You just have to visit sometime and find on your own whether it's for you.