There are two main disadvantages to Cambridge:
-- lack of funding for an expensive degree
-- lack of teaching experience.
If you have full funding you can ignore that problem.
The lack of teaching experience is a bigger issue. You won't get the TA and instructional experience that you probably will in the US, which will make it much harder to get an academic job back home after graduation, in a job market where departments want good instructors as well as researchers. Consider that carefully. Cambridge also has a reputation as being very competitive and unfriendly.
Full disclosure: I'm going to Cambridge. My advisors at my current very friendly and supportive department, made sure I knew about those disadvantages to Cambridge when making the decision, but I couldn't turn down the chance to work with a really great supervisor there.