I was in exactly the same position back in the 1st part of 2001. I was going to uni to study Aerospace Manufacturing Engineering because I was under the impression that everyone does and it was expected of me. I went for sponsorshipin 2001, and when it came to the final debrief the Wg Cdr asked if I'd accept a DE or not. I admitted that I probably would. Offered and accepted it a few months later.
Whilst I did not feel a degree was worth it's weight anymore, you may actually be interested in the subject, and not necessarily the fact that you have a degree. I agree with the coment about the problem with the flying system being congested at the moment. You may find if you go for sponsorship that they don't even want DEs until the system is sorted.
My advice is you keep both applications and just see what they offer . . . no need to make a decision too soon. All I know is I made the right choice for ME! Decide whether or not you really want a degree or just a good time.