Wow. I find myself in very similar circumstances to the original poster, minus having applied anywhere yet.
I have been doing a little research on the subject, so I feel a little qualified to comment. There are plusses and minuses with each route.
The MBA is a well known degree- getting one from a well known institution is definitely a door opener. Its a very general degree- finance, trading, IB are just some of the posibilites possible with it. The flip side is its a very popular degree- there are lots of unemployed and under employed MBAs out there.
The MFE ( here I lump together all the variants- theres no naming convention. Some go by Masters of Fin Eng, Masters of Mathmatical Finance, M. of Quant Finance, etc) is a somewhat new program at most places. A great number of world famous institutions dont even offer this flavor of a degree. Its a very focused professional degree, compared to the more general MBA. Its highly math intensive- mostly stochastic calc, probability, etc. To give you an anecdote, a friend of mine in his second year of the MFE program tells me there were lots of MBAs taking the classes as electives, and most dropped out ASAP.
The demand for these degrees is not 100% known- though many expect it to take off. The role MFEs are going for is much more quantitative. The traditional quant has a PhD in Econ, Math, Natural Sciences or some other quantitative field. A large number of firms simply will not look at you for this role with out a PhD- right or wrong, its a fact. Its then debateable if the MFE gets you into these roles at all. The flip side argument is that MFE is a much more focussed education. The PhD in Chem proves you can handle the quantitative aspect, but you still got to cut your teeth on the finance material. A MFE grad would have this background under his belt already.
I have heard that a much more realistic way to employ the MFE is to get a role supporting the Quants. From there you have to prove yourself, etc.
An informal poll of the MFE's graduating my alma mater puts their salaries significantly south of what I am making- say by 30% or more. Now it may be that its because this isnt a top tier we're talking about, and its a new and thus unknown program, and maybe those kids dont have the work experience I do (front office techie for huge B/D), but I'm really hesitating to jump into something where I would get my career change but at a significant upfront cost (tuition) and a significant long term cost (lower salary).
On the other hand, I want to some day try my hand at entreperneurship, and start a company to play with OPM. I cant do this with a pure tech background, even working on the street. Re-education will be required for me at some point.