I think someone's decision to choose LSE over other top US programs will be based on that person's research interest. I'm into econometrics and I will choose the top 10 (EconPhD.net's overall ranking) over an LSE PhD. Below that, I'll choose LSE.
But remember that if you are into policy research, you know, hoping to work at World Bank, etc. after your PhD, I think the network and experience coming from the proximity of Georgetown will give you a good deal if you choose it.
Also, if you have specific people you might want to mentor you in your dissertation then you choose that program. In LSE you have top econometricians like Oliver Linton.