B.A. vs B.S. would only have an influence upon med school admissions if your B.S. is in an engineering or mathematics discipline -- and then only to compensate for your (perhaps) lower GPA.
Once you're in med school, some docs (like rad-oncs, electro-cardiologists, anesthesiologists, etc) like the quantitative aptitude and ease that most engineering majors display. For example, rad-onc program directors include "engineering major" as ONE of the many factors in assessing residency applications. Keep in mind, however, that MANY other factors are higher on the totem pole (Ph.D., published research in peer-reviewed journal, LOR, AOA, Step I score).
So, basically, if you're in college trying to figure out what to major in, in order to maximize your admissions chances, my advice to you is: pick something that you passionately like so that you can impress schools with a high GPA and spectacular LORs. If this is art history or biomedical engineering, it doesn't really matter at this point (again, BME from Johns Hopkins might be equally impressive to adcoms as art history from UChicago or Yale).