Is there an advantage to have a bachelor of science degree over having a bachelor of arts degree?
It depends. Why are you interested in a BA?
Because you don't have to take as many CS/Math courses?
Because there is another discipline you would like to have a minor in?
..?
If the hiring agent recognizes the difference, then yes. If not, then no. More math and science are important for careers in more technically related (less business related) positions. Also, the curriculum is geared a little bit more towards the technical knowledge you need versus the social.
If you go B.A., may I recommend you take a lot of psychology to flush out the extraverted side in your geek.