B.S. usually is meant for more technical concentration, while B.A. is usually a choice for going into a different field after earning the undergraduate degree, such as going into teaching, or some kind of professional school. What really matters is the selection of courses actually taken and what you understand and what you know how to do; not so much on earning either B.A. or B.S.
my professor who I had for both advanced mechanics and advanced E&M, he was upset because he had to graduate with a BA in physics instead of a BS, even though he had completed all the courses for the BS, because of some technicality.
He got into graduate school in physics, got his phd and is now a full professor of physics. Having a BA vs BS did not matter at all in his case, in retrospect, it wasn't worth getting upset over at the time.
I was a BA physics major for a couple years (I switched to a BS before I actually took any liberal arts classes). So I can tell you about my experience, but I don't know if it will apply to BU or the other schools you're looking at. At my school, the BA physics major required fewer physics courses, and more liberal arts courses. Here's the specifics.
At my school, the BS physics majors had to take the following four "core courses."
Electricity and Magnetism
Statistical and Thermal Physics
We also had to take a two-semester course entitled "Methods of Experimental Physics." During the second semester we designed and carried out a ten-week project; this was easily the most useful class I've ever taken. We also had to take a further upper division physics class, an advanced undergraduate math class, and technical electives, which could be physics and math courses, or other science classes.
BA physics majors only had to take two of the four core courses. Furthermore they could replace the MXP project with a different type of project. And they had to take fewer technical electives, which could be replaced by liberal arts classes. Finally, BA physics majors (like all BAs at my school) had to take four semesters of foreign language.
So what's the difference? Everyone, including my advisors, told me that there is none. However, before I decided to go to graduate school, I tried my hand at getting a job. Many jobs didn't differentiate between BS and BA degrees. But believe it or not, I ran into employers who asked specifically for a BS. Personally I think that if you're looking to go into physics as a career, a BS is certainly a better choice. In addition to the bias among employers, a BS will require you to take the classes that graduate schools are looking for. Grad school will likely care more about the general relativity class you took than about your proficiency at sociology or even foreign language. If you're looking for a less technical career, such as high school teaching, science writing, etc., then these might be good cases for a BA degree. A BA might also be easier if you're double majoring, since your liberal arts requirements can be satisfied by the other major. In fact one reason I was a BA was because I wanted to do a second major in math (I eventually decided to just take an extra semester and get two BS degrees).
Just one additional note. I've found that graduate admissions committees are fairly objective, so I doubt that they'll discriminate according to the word "Arts." If you have a BA, but have taken BS-level coursework, I doubt it will matter at all.