Looking at LBS's requirements, they do look a lot tougher than LSE. When i went to the LBS open day, many of the candidates (with w/e) were also comparing the 2~
LSE's main pro for me is that it doesnt require GMAT and the course costs a lot less than LBS (Around £7k maybe --i could be wrong~~)
LOL Please don't get me wrong. Both are equally amazing schools, either offer will do. TBH, in real life not much diff when managers are hiring so take whichever you got in