I would liken this question to: Which is more prestigious, Columbia University or Dartmouth College? Of course, they are both prestigious schools. One is just more well-known than the other.
Warwick and LSE are both prestigious, and almost equally in that regard. LSE does have the advantage of being more well-known largely due to it being a postgraduate powerhouse, in London and a much older institution. But for those people who care, would view them almost equally prestigious. LSE is the more well-known brand world-wide though.
Remember however that:
Prestige =/= popularity