LSE: more cosmopolitan, better connected to the economics and policy agenda, better international reputation, closer to recruiters. More Nobel (Memorial) Prizes, yadda yadda. Great social scene in a City with a better social scene. LSE without a doubt.
Before you ask - I'm not LSE, I'm proudly Kings, they think they have a rivalry with us (they don't) but I have many LSE friends and it opens A LOT of doors. It is WORTH the extra cost.