<p>It also turns on how much you know about what you want to study. In three years reading maths at Cambridge, you will not take a single subject paper outside of the math department. This can be a good thing or a bad thing, depending on you. </p>
<p>I got to MIT convinced I wanted to major in pure mathematics. I was the captain of my high school math team, and president of the math club, and I knew that I wanted to study pure mathematics. Then I took my first real pure maths course at MIT (Analysis I, 18.100). We started by spending 2 weeks and 8 pages of greek letters proving the existence of the rational numbers. Today I have a small daughter. From the time she was two years old, she was quite comfortable with the idea that she could eat, say, half of a cookie. I found myself frustrated focusing so much energy on proving the existance of fractions, when I was prepared to accept their existence quite comfortably from the age of 2. I concluded that pure mathematics was simply too much mental masturbation for me, and that I needed to change major. </p>
<p>That was a fairly straightforward process at MIT. It would not have been so at Cambridge. I also found that the training I got at MIT in defending my ideas outside of my major field of study was very useful for my life. For example, I took an undergraduate law class at MIT, that exposed me to a way of thinking that was very handy in defending my technical ideas. That again would not have been possible at Cambridge. For those reasons, MIT would be my choice, but your mileage may of course vary.</p>