OP’s school is UCSB, and the OP can take all of the same courses for the BS versus BA major, except for having already taken the physics sequence that is accepted only be the BA major (and none of the upper division chemistry courses at UCSB require the more rigorous physics sequence that the BS major specifies). This was noted in the OP’s other thread at http://talk.collegeconfidential.com/science-majors/1828984-chemistry-ba.html .
Perhaps someone who is familiar with chemistry PhD program admissions and chemistry-specific employment can comment on whether the degree title or the different physics sequences actually make a difference for a chemistry degree.