You won't ever get turned down for having a BS, but some jobs do turn you down for having a BA, especially military or defense contracting companies. At all of the schools I've looked at, getting a BA is ensures almost the same job outlook once you get the degree, but is basically just an easier set of courses. I've spoken with several computer science professors and done quite a bit of research on the subject, because I was looking at a BA in computer science at the university of maine, orono.