E-fizz. I imagine it's much the same in flying as in ATC.. it's nice to have a degree and shows that you have the aptitude to digest masses of largely useless information! However, when it comes to actual training one's educational qualifications mean very little - it's whether you can actually do the job that counts and I suggest that simply having a degree does not necessarily mean you would be a good pilot. You simply cannot tell from a persons educational qualifications whether they are going to make it - practical training and assessment are the only things which will. I've seen plenty of very clever people fail in ATC.... and some apparent dummies turn out to be ace controllers (I've got only 2 GCE O levels but work with guys with degrees). I've seen guys who have failed as ATCOs go on to be airline captains... and amongst us we have several failed airline pilots who have turned into excellent controllers.
Good luck with whatever you decide. I can only advise you to do your very utmost to get into a job which you enjoy doing. it's the only way to spend your working life.