I have a Masters in Electrical Engineering (probably close enough for this discussion - the name varies by country and university). In my day you just got a masters degree - the exact field was up to you. I did mine in high-speed ECG analysis by (what were then, very new and VERY slow) microcomputer which led me into the BioMedical field - at least for a short time. I'm now a business process consultant (Disaster Recovery, Business Continuity, Business Process Re-engineering) and Project Manager having also been an Database consultant, development environment consultant and office automation consultant for an IT firm.
My point is that your degree (whatever level it is and whatever field it is in) will usually be good for your first job. After that, all it proves is that you have been able to reach a particular standard of work. What really matters is what you did in your last job or two.
The problem I found with Engineering is that the field changes very quickly and it is almost impossible to keep up to date unless you have a fairly narrow field of specialisation. Rather, after a few years you stop being an engineer and start managing other engineers who have just come out of University with the latest knowledge.
What is absolutely key is understanding the approach to a problem, the ability to communicate with others (especially those in another field - I've needed to talk with doctors, accountants, CEO's, chairmen of boards and milling machine operators in my time) and translate between the language used in the business and technical worlds. The more broad your reading and interests, the better your ability to draw in ideas and concepts from various fields to apply them tho the problems you are trying to solve right now.
I say study whatever field interests you now - in 5 years you will probably be doing something completely different that you have not even thought about.
Susan