Hey Truc,
could you also share your New School knowledge with me via PM?
I'm from Europe, also applied for both schools. A friend is doing the MSc Social Anthro at LSE right now, and I went to attend class with him.
I don't know how Master programs function in the US, but you should be aware that LSE you will also be attending lectures with undergrads for certain topical courses, although you will have a following discussion with a seminar group only comprising of Master students. This is because the MSc is for people who have not studied anthropology before or only within a more interdisciplinary degree. People who do a bachelor in anthro in the UK could move on straight to a research degree MRes, which can then lead straight into a PhD.
Overall the quality was quite good though. In terms of prestige, LSE is definitely very respected, for anthropology perhaps even more than Oxford or Cambridge. They also have a PhD cooperation program with Columbia. But well, of course, you also pay quite a lot at LSE, even more than you would, for example, at Cambridge, at least for anthropology.
In any case, I would say LSE can keep up with many US schools, but what is of course very different is the length of your degree; go to LSE and you should be done with your PhD within 5 years max, in the US it would be 7 or so. And you might not get funding at LSE, but I am sure you know those things.