Both courses are fairly well respected. If you want to go into economics, then go with LSE, but if you don't think economics is for you and don't think studying it is a good idea go with UCL. You will be spending a lot of your time at LSE studying difficult economic concepts and motivation is very hard to maintain if you aren't interested in the subject. I've got friends studying both courses, and you will learn less pure maths at LSE by a significant margin on the joint honours course (not too surprising really).
Just another point to note, the social scene at any London uni is pretty much the same as you will always find people that want to go out or those that don't depending on your tastes and all the universities have similar locations in terms of clubs etc.