I know that both LBS and LSE are both regarded as prestigious also in the US; both being World Top-business schools. I would say that, for what concern the MiM, in the US are regarded as being exactly on the same level, or even LSE slighlty more while if you look at MBA, then LBS is more appreciated (cos it has #1 mba program in the world - LSE does not provide MBA).
For what concerns the Career service at LSE, I know from people doing that course, that is one extra-service (so not the ordinary career help office) specifically tought for the Management dep (they help you contacting MNCs, having interviews, networking etc) , and mostly of the resources are devoted specifically to the MiM, that is considered the edge of the department.
Finally concerning the links to the employment, yes surely LSE has better links due to greater presence for any analyst type job