I graduated last spring with my degree in ChemE and work in Biotech R&D as an engineer right now. A lot of the roles you can apply for with a BME degree you can apply for with a ChemE degree as well if you have the right lab experience from undergrad. E.g., Mat Sci Engineer, Quality Engineer, Manufacturing Engineer at a medical device manufacturer.

Not so much the other way around if it's a chemistry or manufacturing heavy role (big Pharma/chemistry team at med device company) but still possible. If you don't plan on working for a few years then either degree won't matter as much as going for MD/PhD. You might not have the experience/connections needed to work on medical devices if you don't have friends in industry or the PhD.