Is training in Biostats sufficient to get into Data Science?
a question, and then some comments.  First, what kind of market analyst do you want to be?  This field is rapidly becoming specialized, and the answer will affect the decision.  If you want to specialize in the pharma or especially the medical field, the biostat background could be an advantage.

Generally speaking, you need to think outside the box of what you will learn purely as defined by the program, either stats or biostats.  You will need to branch out into areas not defined by either program.  This could include (1) software language, (2) data science problems (Kaggle or external projects run through a campus department), or (3) courses not expressly given in either department, whether it's in "hard" skills like data mining or "soft" skills like marketing.  Ask for exceptions to do things that don't fit the program, but fit your career goals, because being a market analyst doesn't fit squarely into either field.