LSE is the best in Europe for economics. Think teaching and feedback is a bit better at Warwick (since amazing research ability doesn't perfectly translate to good ability to teach). Community will be a bit more insular at LSE and you're likely to have more of a social life at Warwick.
If you look at the unistats for personal feedback students don't appear to give a very positive view on being satisfied overall or that lecturers made things interesting (about 60% or so). So while you'll likely be stronger at economics if you're at LSE, Warwick will give you the better educational experience
Warwick is still extensively recruited by economic consultancies (Warwick is very strong in IO, think it's only second to LSE) and financial firms as well as IBs, though less so than LSE. LSE's contacts and networks is going to be better.
I can't be bothered to look at the modules but from a brief look they use the same textbooks for the macro and micro modules