Well that's a pretty tough choice,both the schools are pretty well known & prestigious. I have some fair knowledge about the MiM at LBS and LSE, so i can give my 2 cents about them.
Making a quick and preliminary call by checking out the FT rankings is difficult as it puts LBS at rank 10 while LSE is un raked (most probably because 4 years must have passed before a schools MiM can be included for rankings), but i am pretty sure LSE would also come up with a pretty high rank when it is listed.
A more in-depth comparison shows the following differences:
1) LBS is a fast paced 1 year program while LSE is a more theoretical 2 year program. In fact LSE describes its MiM program as "unshamedly academic" and touts it as a program to build a sound business foundation.
2) LBS costs around around 27500 pounds while LSE is a total of almost 50000 pounds, of course it is a 1 year vs 2 year program
3) LBS core values are more towards leadership and dynamism while LSE preaches a more in depth critical thinking approach as can be observed via its core value "Analyzing the cause of things"
4) Base Salary of 36,295PS & 97% accepted a Job offer within 3 months of graduation for LBS
86% in work/further study 6 months after graduation & 38,100 pounds avg salary for LSE
So in conclusion if you are looking for a faster way to get a good business education and get into the industry - LBS is a good choice, while f you want to build a strong business foundation and don't mind a more in-depth 2 year course LSE would be optimal.
You can check up on
https://www.mim-essay.com/lbs-mim-review.html and
https://www.mim-essay.com/lse-mim-program-review.html for a detailed review on LBS and LSE MiM and make a more educated decision.
Hope the answer helped.