I'd have prefered Cambridge because I wanted to get out of London, I'd have preferred the collegiate system because it seems more friendly (although haven't actually visited LSE yet) and for the Oxbridge reputation (but I got rejected!), but LSE because I have the exact course I want, and I'd prefer to have the LLB than a BA at the end of it (although I'm not entirely sure what the difference is!)
That said, seeing as I was rejected from Cambridge, I'm now determined to think LSE is way better, so go to LSE!