Fuqua’s MMS program is basically a shortened version of the MBA program. The MMS students take the core courses that MBA students take plus a select few electives. The professors, teaching method, and assignments are similar as well.
Duke’s MEM is offered through the Pratt Engineering School. I’m not sure the curriculum, but I would presume that they have an engineering focus. Additionally, whereas MMS take students with any undergrad majors, MEM would pull more from engineering undergrad degrees.
Given Duke’s strong relationship with the consulting and finance industries, both degrees have access to consulting and finance companies. Although the exit level to consulting and finance companies are comparable to those of undergrad exit (associate/analyst level).