I graduted from the MA program. In terms of the electives - the above comparison is incorrect. 1) There is a good class "Statistical methods infinance" offered, where you can can learn about portfolio management and optimization. And they obviously teach you Monte Carlo simulations there.
2) "Stochastic Methods in Finance" is not another name for "Stochastic Calculus". They are 2 different classes and both are required for the digree. You take the "St. Calculus" first and learn the math behind it. And then in "St. Meth. in Fin." you learn how to use stochastic calculus for pricing and modeling in financial industry.
3) It's useless to compare coursework in my opinion, since you can always take any class for the FE program as elective being the MF student. You can also take up to 1 class per semester in business school. The same about programming - we had many students taking programming classes.
4) One problem with the MF is that it is only 2 semesters vs, FE 3 semesters - you miss an important for your future career summer internship. Although if you're lucky enough to get a good job without an internship on your resume, you end up saving money for tuition and half a year of your time.
You said there is Derman in FE? We have Karatzas there, not bad either.
In general, the major difference is definitely not the coursework, since as Columbia student you can pretty much take any classes from many schools - SIPA, CS, Statistics, Engeneering. It is supposed to be only 1 year - you have only that much time. However if you think about it, you can stretch your program in 3 semesters, take more electives in whatever field you want and these 2 programs will be pretty much the same. And you can even get the internship in summer - employers don't really distinguish which program you're from - MF or FE.

The major difference in the kind of people admitted to the program. In FE you will mostly find fresh graduates in their early 20s - it is a full-time only program. In MF there are many working students - all core courses are offered at night and can be taken part - time, they are older and don't remember any math

(to be precise there is about 50%-50% mix of school graduates and experienced people).
I heard NYU has the best program of it's kind. (And the difference mostly comes form the career center). Remember, whatever program you choose, much more depends on you personally, rather that the program you're in.