Hi,
In my experience, it is a bit easier for engineers who already have the math training to step into learning biology and become a biomedical engineer. Mechanical engineering prepares you to design devices as an engineer in industry, whereas biochemistry prepares you to do research on biomolecules. If your interest is in the intersection, you can choose either major and still take the core courses from both majors and better prepare for your future career.
Ying-Ja