London School of Economics vs. London Business School

you're not really comparing apples to apples. the LSE Msc is a pre-work program (most of class will have no full-time work experience and be coming straight from undergrad) while the LBS MiF is post-work (average FT experience is actually higher than for the MBA at 6 years). The LBS equivalent would be the MiM. Access and placement for the Msc and MiM are very similar and you would have access to all the top banks through OCR, I don't think you can go wrong with either school. The programs are different though, the MiM is a general management program while LSE is finance only so depending on you existing finance knowledge, that can be a consideration. Both have great alumni network, although LBS has the advantage of networking with current MBA / MiF students (I am biased here, went to LBS for MBA and was mentor to a few MiMs). LBS is twice as expensive through (and even more for EU students) so although I would strongly recommend LBS for other programs, I am not sure the additional tuition really brings that much added value. In terms of prestige, both have very good reputation and are viewed quite highly. Not that it matters, but since it is much smaller, LBS is nowhere near as well-known outside of the business community (a lot of people think / assume LBS and LSE are the same).

BTW, both the MiM and MiF are 1-year program. The MiF can be done over 15 months (or perhaps even 18) to enable students to do a summer internship, but very few end up doing that.