I was also accepted to Oxford's MSc in CSP and LSE's MSc in Social Policy and Planning. I don't know much about Heinz, but I am deciding between those 2 schools and UPenn's Social Policy Program. For me it will come down to funding (of course), strength on national and international reputation, job placement, and curriculum. By far, in terms of international social policy reputation - Oxford and LSE are strongest. LSE's program has a long history and strong curriculum. Of course, Oxford is...Oxford and has instant name recognition much like a Harvard Kennedy School.
At the end of the day, for me its about being prepared with the strongest skill set and leaving the program with a strong footing to be able to secure the job I want. So in the end, if Oxford comes through with funding, I will go there.