I think it's really a question of which direction you are planning to take your career, if as you say you want to become a web designer then I would imagine that a BA. Would be more suitable.  However, if you wanted to become a web developer (more emphasis on code development, relatively little focus on graphic design) then like me, you would probably find a BSc. To be more suitable.

Ultimately it is down to the content of the course itself and how well this matches with your own interests and career plan - I would strongly recommend attend an open day for any degree course you are considering and making sure you ask lots of questions because the promotional literature for degree courses tends to be a little bit lightweight.