Do you want to design new drugs? Or new drug delivery systems (implantable materials or nano-devices)?
The former is more biochemistry/molecular biology. Engineering is more process -oriented and more likely to do the latter.
Do you want to spent 100% of your time in the lab doing research? Or do you want to participate in hands-on patient care?
If your goal is to spend 100% of your time in the lab, then a MD/PhD is the wrong path for you. MD/PhDs split their time between research and clinical duties. Most splits are 30-70 or 50-50 lab/patient care, though at a few very high powered & generous programs the split is 70-30. If you want to spend 100% of your time on research, then you really want a PhD. (And a PhD will get you into the lab about 7 years sooner than MD/PhD will since you get to skip the 4 years of med school plus the 3-7 years of residency.)
One consideration–engineer majors tend to have a more difficult time maintain the high GPA needed for MD admissions. (3.7+ was the median GPA for admitted MD students last year. It was even higher for MD/PhDs.)
As @bopper mentioned, you don’t need to major in a biomedical engineering type field to work in the BME industry/research. ChemE, EE, MechE, material science and physics majors will also allow entry into biomedical engineering jobs. Many entry level BME jobs require a MS degree.
(I’ll mention here that D1 was a physics major and she was able to apply for MD/MS programs for BME without any issues. D2 spent 2 years doing BME research & was offered a place in a big name MS BME program before she went to med school; she was a biological neuroscience & mathematics double major. IOW, there are plenty of ways to get where you want to go by taking additional coursework and getting involved in research that emphasizes your focus of interest during undergrad.)