I don't think it is an MBA vs an MFE issue of whether someone will progress to a "trader" in their organization or any other senior position but more of an issue is their "whole person" personality traits.
The "whole person", the sum of their life experiences, learning ability, work ethic, personality, contacts, and political ability, get evaluated by management and if you add more value then the other people trying to get the same job, it's yours. There have been many studies to suggest that technical knowledge is responsible for less then 25% of your career success, even in technical positions.
My suggestion is to try to be knowledgeable and actively involved in as many fields as possible to build and refine the "whole person" view. As a student it is easy to join in activities and clubs at campus but most MFE students do not. I remember when our famous ex-President of Quantnet, Jimmy "the Phoenix" Chin called me to attend meetings of the Graduate Student organization, we were looked on as novelties as they had not seen any involvement from the MFE students.
If you believe you are too busy to attend non academic events now that you are students, how will you find the time later when you are working 10-12 hours, have a family waiting for you at home and each event cost real money to attend? Playing on your company basketball team or a night out with your workmates once a week will further progress your careers then your ability to recite the solution to BS equation.... which you should know by now anyway....