Generally, people with MSFE get into analyst roles at investment banks.
MSFE is relatively a new course. Before that investment banks used to hire quant Phds, and people graduated from top 10-15 schools for analyst roles. MSFE is a course just created to get you trained for analyst roles.
In a typical investment banking firm, analyst works for 2-3 years gets burnt out by the work pressure of say 80-100 hours/week. If analyst stays there for 1-2 years more he would progress to associate role, but he doesn't have any energy left by then. He prefers to take a sabatical for 2 years in to B-school.
If he is lucky, he leaves investment banking and gets into private equity or hedge funds. If he is not he joins back as an associate. Generally people with MBA finance join investment banks at the associate level.
Associate generally manages a team of analysts. Checks the valuation models prepared by analysts and help prepare pitch books.
If you are completely sure to make a career shift to finance, best way to go about it is MSFE and then take job as analyst / trader. Simultaneously go for CFA.
If you are unsure about career switch, MBA will open whole range of opportunities. MBA can be fitted into many different roles as compared to MSFE.
Best of luck.