Hey,
I wouldn't really say I am a newbie at this forum since I've been silently gathering lots of information during my application process, but I figured this is the right time for my debut!
So the story is that somehow I have been able to receive offers for both of these programmes, and I was wondering if someone could give me some opinions about the comparison between the two.
SHORT VERSION:
Ok so I got into these two programmes so I just want to hear people's views on the unis and programmes

Long-term goals are consulting and MBA
LONG VERSION:
As for myself, I aim to go into consulting, and I am at a position where I am able to pass the CV screening for the major consulting firms (McKinsey, BCG, AT Kearney) within my country without the Masters programme. That being said I don't feel very confident about the case interviews, so that would be my main recruiting problem. Also, I wouldn't necessarily say I am bad at interviews, but I am not amazing either, so I think more networking and variety of experiences could help me in terms of communication and having more things to talk about.
So in the end, what I primarily seek is a programme which gives me plenty of opportunities to practice and hone my case study interview skills, opportunities to possibly consider different career paths (hey, I'm still young, shouldn't be too narrow-minded... except for Finance, never really been my thing), networking opportunities, and lastly a help me with my odds at landing a top MBA. I know that in the end getting an MBA or a good grad job is up to me, but surely it helps to increase your chances even if by small margins.
I like LBS for the opportunity to meet and network with people from their other programmes (mainly MBAs), who are well accomplished, and their great alumni base. Since the school is so focused, you can see that the faculty is really cherry-picked, I saw people with some impressive backgrounds. Lastly the programme seems to be quite interactive with a variety of group projects, international/career treks, and company visits. I am an international/EU (dual citizenship) student coming out of a UK uni, so I got quite used to the UK-style of academics, so maybe trying something different could give me some fresh outlook (don't really know if this is a + or -).
LSE is quite appealing for the curriculum, which is more focused to my aims, and the class size, which is about 50 people. I did some LinkedIn stalking (no shame, you do it too!) and the students coming out of this programme have some amazing profiles, so I wouldn't say that one class is "cooler" than the other.
In terms of reputations, I am struggling to figure out which of the programmes would give me an edge during MBA applications (as I assume both unis do well in terms of screening at major firms).
Anyways, sorry for the long post and hopefully we can generate some constructive discussion! (please no "LBS all the wayyy!!" without stating the reasons). Also, if any of the potential applicants want any tips then don't be afraid to ask me, even though I cannot guarantee that my advice will be relevant given that I will only speak from my personal experience, but I promise I will do my best to help!