MFE alumni here. I have also worked with a few MMF’s.
MFE students take courses on economics and a few MBA electives. MFE graduates from my year went into IB, S&T, Risk Management, Equity Research, Commercial Banking, Actuarial Science, PhD, etc.
On the other hand, the MMF courses are a lot more quantitative and requires programming. The MMF prepares for careers in quantitative finance, risk management, model validation, etc.
Both programs are well-respected by the industry, especially on Bay Street. I like to view MFE’s as well-rounded analysts who have the capability to understand the technicals and to bridge the gap with MMF’s quants who are more specialized.