To start, I did the MSc in IR at LSE, but I have a lot of friends who did the programs in your list. LSE is comparable to the top tier of American IR/professional schools, which would be:
Georgetown - SFS
Princeton University
Columbia - SIPA
Johns Hopkins - SAIS
Tufts - Fletcher (maybe)
Below these would be:
George Washington
University of Chicago
Yale University
Monterey Institute (for security studies - especially nuclear policy)
And below those I would group:
American - SIS
University of California San Diego
University of Pennsylvania
Okay, some differences between U.S. and UK degrees. The people at the U.S. ones - particularly the top tier - will be older than at LSE, Oxford, or SOAS. They are typically professional schools and want students with some work experience under their belt. In addition, you get more hand-holding from professors in the U.S.
In terms of international student population, LSE is vastly higher. My IR degree had around 70% foreign students (many of these were Americans however), while U.S. degrees typically have around 30-40%. That said, I've met more Africans who went to the American schools, so that perspective unfortunately is a little weak at LSE.
Job opportunities are more difficult to discuss. LSE obviously has better connections to Europe and the UK, but studying in New York or Washington, DC brings incomparable benefits when it comes to making connections and networking. Then again, as an American, I found it very difficult to find a job in the UK, so that definitely has something to do with it.