To answer your question in very broad terms:
MBA - Focuses on a more holistic approach - a little bit of finance, a little bit of marketing, a little bit of accounting, ALOT of what you choose to concentrate it (your specialization). MBA programs generally last 2 years but depending on where you apply you will get shorter programs as well. The MBA's goal is to give you a solid grasp and understanding in various areas of business economics, accounting, finance, statistics, strategy, and so on.
MSF - Focuses solely on the finance discipline by taking different approaches to it. MSF programs generally last 1 year. The MSF's goal is to prepare you and give you a solid understanding of various areas of Finance such as Corporate finance, Valuations, Financial markets, etc.
So essentially if you choose to specialize in Finance in an MBA you will have all other types of knowledge which will be adding value to your main specialization. In an MSF you will be focusing primarily on the finance aspect and adding value perhaps by doing some economics, accounting, but no marketing. So the skill sets you obtain are different. A good analogy is the general physician and the neurologist. The general phsyician knows about dermatology, gastroentology, x, y where as the neorlogist knows most about neurology. An MBA will probably learn about the black-scholes equation and its uses but perhaps an MSF will know the components , functions and can calculate the equations.
Your spectrum of choices post- degree will be limited depending on the program you opt to do. As an MSF it is more than likely that you will enter the finance function of a firm. Whereas an MBA leaves the playing field more open given that you have knowledge of every component of business and a even stronger understanding of your specialization.
I think that the value of having degrees is pretty much dependent upon your choices. I am sure there are some overlaps but how you manage your electives would be key. Also, both might be different experiences in different nations, schools, and thus, you will meet different people - expanding your contact database. So the value is there - just depends on how much of your status qou you want to give up.
Hope something helped.
Jas