I made this decision about a year ago. I'm American, and I'd wanted to go to Oxford since I was little, but I chose Cambridge and didn't even apply to Oxford. My main reason is that Cambridge has a one-year program and some specific faculty members who I want to work with. Oxford's program is two years. I can see benefits for both if your ultimate goal is law school. Cambridge's program will give you the depth in IR and will get you to law school more quickly, but Oxford's program will give you more time to get ready, take the LSAT, and work on applications. If you're looking at going into international law and want to try some at the graduate level, you should look at the course offerings this year for each school; they'll probably change next year but you'll get some idea. I've heard that Dr. Weller at Cambridge teaches a good International Constitutional Law course and I'm sure Oxford has good courses on it as well.
You should also look into LSE, KCL, and SOAS. KCL has some really interesting programs (like international intelligence and security).