I looked into the Sloan Fellows program a bit. Since you already have an MBA, you'd be going for the Masters in Leadership degree that each Sloan Fellows school offers.
I researched the one at MIT fairly thoroughly and also researched the LBS one a little too. I also got to talk with a Sloan Fellows grad from each of those schools. One thing I found interesting is that for my friend who did his degree at MIT, his class was 70/30 company sponsored vs. self sponsored whereas my friend at LBS said his class was definitely more self sponsored. I've never done any research to see if this is a trend, but I definitely think having so many company sponsored students changes the dynamic a bit. While I wouldn't say that Sloan Fellows is like a fun camp since it is very rigorous and hard on sleep, I can imagine how being sponsored can change the motivation of some to be fully committed.
If you google "Ian Lamont" and "Sloan", you'll find Ian's blogs where he talks about his experience. I also chatted with him on the phone and he has a lot of information.
You mentioned the cost, and I can't remember the LBS cost, but the MIT Sloan Fellows cost is really hard to stomach--$121,000 for 1 year.
I asked my friends about the recognition of the degree, and for those who got the Masters in Leadership, my friends inevitably always had to explain it. But once people hear the prestige of the program, there are usually no issues after that. That said, I always think that if you want to work in the US, you're almost always better off going to a US school in terms of recruiting (obviously one school may be preferable to you for other reasons relating to other parts of the experience.)
You should also look into speaking directly with the school. I spoke to Marc O'Mansky at MIT and he is very candid about telling you whether he thinks you would be a good fit, and will answer all your questions.
Ultimately, I decided that I wanted a regular MBA, so I didn't go for the Sloan Fellows. I am looking to change my career a bit, and also I didn't want to do everything in one year.
If you PM me, I can also give you details of my friend who did the LBS Sloan fellows program. Sorry, I don't know anyone who did Stanford.