EE with minor in BME is easier for finding an industry job immediately after college because of the broad nature of BME training. However, the broadness of BME could be mitigated by an EE-focused BME track (e.g. signal processing), a good project portfolio, and an industry internship or co-op. The industry work experience ends up being the most useful for finding an industry job.
I've seen multiple people build their engineering project portfolio with research that includes MD collaborators, and who choose medically relevant industry internships (Stryker, 3M, Boston Scientific, Medtronic). A couple MD/PhD programs specifically favor applicants with this experience. One generic piece of advice is to take a reasonable courseload! The time/stress of really difficult courses can get in the way of both keeping the GPA good and having time for research. The really hard junior/senior courses aren't even that useful for getting industry jobs. Definitely take a reasonable courseload in your capstone/undergraduate thesis year, especially if you are also writing MD/PhD applications.
That doesn't specifically answer your question of major choice because it depends on the institution. Some specific variations to look for:
- If there is a BME track that aligns with both industry and MD/PhD, and has good coursework overlap with an EE minor.
- On the other hand, if the BME minor requirements overlap with premed coursework.
- Whether the BME or EE dept has extremely hard classes, low average GPA, high attrition, high student stress. Are there 'weedout classes'? If so, try to avoid taking them at the same time as pre-med weedout classes.
- Which dept. provides institutional support for an internship/co-op.
- Which dept. provides better resources for students who want to do have a research-based project portfolio.
By the way, you might also find research mentors with projects that match your interests in the "bio" tracks of other departments like electrical, chemical, mechanical/mechatronics, biomaterials, applied physics, applied math, CS, computer engineering, etc. You don't have to be in the same department as your undergrad research advisor.