DH is a psych professor and I'm going to let him write here:
I advised undergrads at the large state university where I got my PhD and served on the grad admissions committee there. At that university, the only difference between BA and BS was that the former required a couple of foreign language classes and the latter required a couple of math classes instead. The psych curriculum was the same. In terms of admissions to the grad program, I don't recall a single time that I or anyone else even paid attention to whether it was a BA or BS. We might look at quantitative reasoning ability, but more typically by looking at math classes and grades and at the math portion of the GRE.
If he's thinking of graduate school, the most important thing is to go to a place where he can start being a research assistant for a psych professor's research, and to do so early. The more he can do to work with researchers in an intimate lab setting, the better. Other than good academic indicators, research experience (and the good letters of recommendation that come with it) is the most important factor.
I should also note that this was the case for applicants to the clinical PhD program. Applications from students genuinely invested in helping people were a dime a dozen. The ones that stood out were always those from applicants who had lengthy research experiences in one lab. In addition to the exposure to cutting edge research and the lab discussions that lead to researchers homing in on the boundaries of knowledge in the field, that lengthy exposure shows grad committees that you're dedicated to the field, thrive in situations where you are trusted to complete lots of tasks without constant supervision, and aren't fazed by the tedium of research. Even for students going into purely applied fields like counseling benefit from this experience and are better students for it.
Final piece of advice if he's thinking of applied fields: try to find programs with an applied practicum. At my undergrad institution (a small liberal arts school) I spent two years volunteering at a local crisis hotline (in addition to my 3.5 years in research labs). Students at that institution can also go to these community organizations and complete a senior practicum by volunteering there and writing a paper connecting their experiences to their coursework. If I had wanted to go into counseling, that experience would have been an important undergrad experience.
The TL;DR version: what your son does to gain experience outside of the classroom is FAR more important than the psych curriculum.
