Glad you found the comments helpful. Interesting questions...
I should probably disclose that I was deciding between LSE, SOAS, and SIPA, and went with the first one, of course.
Well, first off, yes, you have the acceptance rate stuff correct. In certain US programs, 50 of every 100 students gets accepted, depending on demand, application pool, etc. Particularly for foreign students, US programs have shockingly high acceptance rates. Columbia undergraduate, law, and business, for example, are all very competitive, but SIPA (which includes the MPA and MIA programs) falters on that. But, like I said, it can be a good or bad thing depending. More diversity in the student body, but less caliber of student.
As for the MBA feel, that's tricky. US IR programs don't necessarily require the finance, accounting, and more general quanitative studies that the MBA programs do. SAIS is very quantitative based, having strong connections to the World Bank, IMF, and other development/financial institutions. GWU highly emphasizes real world experience, and almost pushes its students into internships during the school year and the summer recess. However, Georgetown and Fletcher, from my understanding, don't have this emphasis, being more focused on security studies and law, respectively. That said, any school you go to, US or UK, will allow you to take greater concentrations in quantitative approaches. It's a question, however, whether they are built-in to the system, are sufficiently supported by the faculty, etc.
As for LSE, I would say on balance it resembles a more traditional academic Masters rather than a professional degree. You still walk out with great analytical abilities, but it's not coupled with the leadership and networking "training" you get in an MBA. If that's your desired focus, you should perhaps consider an MPA, depending on how you see your future career. I should mention that my picture of professional degrees is pretty colored by my friends, whom I see study a lot, but also drink and socialize quite a bit too as part of their education (I'm being serious, partly for the MBAs).
I am glad that I went to LSE, although towards the end I wish I had another year. I'm thinking it's because I had a really enjoyable academic experience and wanted to keep it going. Now, however, I do have significantly less debt than my peers. As for the job hunt, much of my friends' experiences have depended on where they are. Most LSE non-Americans were able to find a job pretty quickly. Come to DC, however, and the DC-based IR programs really have an advantage. Alumni of non-DC-based programs, both American and British, all hit the same problem coming here: temping for a while, trying to get their feet in the door, several months of looking for a job, until the market finally snaps them up.
Many people that I have met in everyday settings automatically assume that I did economics at LSE, which has largely been a positive thing. Keeps them off-balance when evaluating my abilities or it's good as an icebreaker. In job interviews, however, LSE is definitely known as one of the best places globally for IR.
As for how LSE stacks up, it is more or less equivalent to an Ivy League school. I don't know how much that really means though. No one thinks of LSE as an Ivy of course, and the "polish" on the Ivy's has diminished somewhat anyway.
I realize this is a lot of stuff all thrown together. Between Fletcher and LSE, you can't really go wrong. They're both great schools. Fletcher obviously has a great concentration on law, although they have decent scholars on more security related topics. The drawback is that you are in Boston (well, not even), removed from the major centers of IR and therefore from certain lecture/employment opportunities.
LSE, like almost all UK universities, suffers from a lack of funds compared to US schools. So, expect Tufts to have much better facilities. But, you are in London, get great speakers, and have a wider range of excellent professors specializing in more topics. You can also draw on LSE's other departments and courses.
Of course, the teaching system is entirely different, and depending on the structure of your previous education, you may get more out of one system or another. If you can give me an idea of what your educational structure was like, I might be able to give you some better advice.