The advantage and disadvantages would depend on what the person wants to do after the BS or BA. If continuing to graduate school, it would be best to speak with an academic adviser for the graduate program in which the person wants to enroll. They could tell you what the preference is. The most basic difference is BA degrees usually have a foreign language requirement and BS degrees do not. Hope this helps!
It all depends on your post graduate studies. If you want to go into clinical psychology BS would seem to be more appropriate, whereas family psychologists are more appropriated to a BA degree for they use language interpretations in therapy. The degree only differs in the additional subjects, the psychology stays the same.