I was a BME in undergrad at a top-5 engineering school. Applying to med school this year.
First, it definitely gave me a lower GPA. I have a 40 on the MCAT, but a 3.35 GPA at my home institution (a semester abroad brought it up to 3.41). And sure, I could've worked harder, but I know an identical work ethic would've given me a 3.8+ at a different school. To give you an idea, the average grade in my first math class (Calc II) was 2.07, and only 8% of people in my orgo I class made an A. My GPA was good enough for high honors, but of course it's low for med school. BMEs make the highest scores on the MCAT by major, so it helped there. (hopefully it's enough to pull up my GPA...). However, BME gave me an incredibly good work ethic. I'm in a PhD program now, which is much easier than undergrad, and I've worked incredibly hard in lab and kicked butt in research. I'm not a naturally gunner-type person, but my undergrad degree made me work, so working hard is now average.
Finally, it made me think about problems a different way. I now think about things very quantitatively- physics will never make you think the same way when you drive again. Multivariable calculus will make you better at thinking in the abstract. Programming will make you understand logic. Statistics will make you think probabilistically. And all of your engineering courses will make you think "How could I do or design this better?" in everything you do.
Would I do it again? Well, ask me after this application cycle 🙂