If you got into universities like Oxbridge/Ivy League, you will be pushed extremely hard academically. Wouldn't this cause you to miss out on the "traditional" uni experience? By this I mean hanging out with friends, partying, gaming with friends etc.(purely my personal definition, feel free to disagree) Not that universities mentioned above would not provide that experience, but in a slightly different way. For example, I understand in Cambridge there are common rooms for students to interact and such. But in institutions such as these the time for leisure/entertainment will be decreased due to the increased workload and expectations of academic excellence.
Therefore is it better to get into these unis for postgraduate? After you have "enjoyed" university at an undergraduate level and wish to settle down in serious pursuit of your studies. Furthermore for some of the universities mentioned is is their graduate school education that defines them and gives them the revered reputation it holds. *this may only apply to some people, if you think that the university experience you want is different feel free to disagree and contribute to this discussion.