I just finished the MSOR program and know a lot about the other two, MSFE and MAFN. First of all, they're all pretty much the same, but I'll fill you in on the minor differences.
MSFE: Master of Science in Financial Engineering
This degree is 36 credits, with a large amount of required coursework and then electives you must choose from a short list. Everything you do will be extremely applied and will be very, very quant. The other benefit here is that when you put the MSFE tag on your resume, everyone knows exactly what you did because the program is so specific.
MSOR: Master of Science in Operations Research
This degree is 30 credits, with a small amount of required coursework and lots of space for electives. In short, this degree lets you tailor the masters to your liking. Of course, you have to fulfill certain requirements, but some of your electives can range from the most quant FE courses to the most qualitative business school or international affairs courses. The reason I liked this program is because I wanted to have a solid quantitative edge, but I didn't want to be a pure quant. For this program, you would need to list an area of specialization or your relevant coursework on your resume. Specializations could be anything from optimization to applied probability to financial engineering.
MAFN: Master of Arts in Financial Mathematics
This degree is 30 credits. This program is more based in statistics than the other two. You'll be doing time series, regression, and numerical methods a bit more than in the other programs. Other than that, it's just about the same except that courses are offered through the math department rather than the engineering department.
I hope my message is clear: it doesn't really matter which one you do at the end of the day. It just depends on what you want. If you want more statistics and you don't like engineering departments, do the MAFN. If you want a very regimented quant program, do the MSFE. If you want a flexible program you could tailor to FE in a way of your choosing, do the MSOR. There aren't any differences in hiring statistics for finance jobs. It's a bit easier to go into i banking or consulting from MSOR (assuming you take corporate finance or strategy courses), though, if that's what you want. Otherwise it's all the same.