Generally, financial engineers look for quant jobs heavy in math and/or computer programming. They develop pricing models, trading strategies, etc and write software to test and implement them. They can be traders, portfolio managers, analysts, developers, etc.
MS Finance is for financial analysts, portfolio managers--jobs heavy in finance but not necessarily math. And generally no programming involved.
MBA's are for people with no idea of what they want to do. They go into a very broad field called "consulting", which is like saying your favorite thing to do is "stuff". They study useless subjects like Human Resources, Organizational Behavior, and their curriculum generally has about 10,000 different subjects packed into 2 year programs. So you leave with a little knowledge--most of it useless--in a lot of subjects. MBA's are one of the few graduate degrees where school and ranking matter, unfortunately. Probably because every school in the world has a program.
In all seriousness, you just have to get an idea of what kind of job you want, and then match your graduate studies accordingly. Do you want to be a trader? A programmer? A business analyst? A J. Crew model? You tell us, and then we can tell you the best type of program.
Hope that helps.