My Hotel and Restaurant Admin degree has served me well over many years of flying!
I instructed quite a few years in military basic and advanced flying and saw almost all types of degreed students. Embry grads, AF Academy grads, barely grads, etc. Degree made no difference in flying ability generally, especially in advanced tng (T-38). Once you get beyond the high cambered, straight wing stuff (T-37), innate ability takes over.
Sometimes the guys with CFI, CFII, etc backgrounds had the toughest time. They smoked the academics, and tore up basic flying, but once the speed and complexity of the flying increased they no longer had an edge on the rest. They were generally great pilots who did well, but some were frustrated that their pace of learning slowed. Wasn't that they stagnated, it was just that everyone was in a new arena, including them and they had no experience to draw on that was similar to the faster jet. Those with hands and the ability to think quickly did the best in the T-38, no matter what their degree or flying background was.
Move on to airlines now. No one knows or cares what the degree is, and no one even knows what your flying background is unless it comes up in conversation. You gotta do what you gotta do to fill squares to get the flying job you want, but I'll agree with the others that the flying degree doesn't seem to make a hill of beans difference. Maybe some that have been airline interviewers can chime in, but it has seemed for years that it's just been experience, hours, and some type of degree are the prereq's.
I didn't go the civilian route, so I don't know the ins and outs of that path, but I've flown many years now with civilian trained, military trained, both US and non-US trained pilots, and generally if a pilot has accumulated enough hours to get the job, he/she flies the same as anyone else.
Get the hours you need. Get a degree in something you like and will serve you in the future.
My 2 cents,
Fugawe