A Master's in Finance is a graduate degree that emphasizes development of innovative leadership in financial management, according to MIT Sloan Management School, a leading provider of a Master in Finance program.
A Master's of Business Administration is a common business graduate degree. It is a broad-based business-management degree but typically offers students specialization in areas like finance. The Guide to Online Schools points out that an MBA in Finance adds to a business degree by teaching students to make high-level risk-and-reward-based financial decisions.
If your intention is to become a professional economist, you should opt for a Master's in Finance. If you are interested in broader business-management areas likely to involve high-level financial decisions, you should obtain an MBA with finance emphasis.