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it is not good or bad, but fit or not only........and the most important point is indeed.......get the term "finance" on the CV for job search.
If you afraid that you will repeat something that had studied in part of the master......the very first thing you should do is: apply a master in a similar but different field, unless the program is super solid.
For you case, it can be something like (Risk and Stochastics), (Financial Mathematics), (Computational Statistics), (Machine Learning) or etc.....if you really want to same field, and have a advanced statistics master, a better idea will be applying to a scienec and engineering school, instead of a social science one....or a research master like MPhil.
Columbia one for sure doesn't count - it is a program for non-stat background student (look at the admission requirement), and the first half of it sounds to be at senior bachelor level (look at the course outline). The LSE is more advanced from this point of view.
P.S. At the end, the reputation of LSE vs Columbia won't matters.............both will get the interview, and the rest depends on oneself instead of the name of the school.
and if you have a few years of experience when you go back, the school name no longer matter much.
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