I'm not familiar with IO so I can't really say. My assumption is that LSE would be much stronger in IO; RePec (which is not necessarily the best way to look at rankings) has them ranked at 11 while Rochester doesn't show up. I'd personally take a couple of hours to look at CVs of current professors and recent graduates of both schools to sort of get a sense of what is viable and what isn't.
By MSc I'm assuming you're talking about the EME? What % of graduates receive distinction? Also, 30k pounds in tuition fees is nothing to scoff at. From what I've heard, competition is extremely tough (everybody wants to get a top 10 PhD), and its hard to get strong letters since the program length doesn't reach a year. I've also heard that PhD stipends are pretty bad, and London is obviously expensive. That being said, LSE is probably comparable with top 10 programs if the U.S. in terms of placement, but I'm not sure if that is in regards to training or because they have the reputation as probably the best program in Europe (so input quality is high). I don't think either choice is necessarily better than the other, it just depends on your personal goals and where you think you can place.
Again, I'm not an expert so take everything I say with a grain of salt.