I managed to have a great career (so far) with a degree in aviation management. I was lucky.
If I could go back, I'd get a degree in finance, computer science, or pre-law, or building science, or darn near anything. The only thing my AM degree was good for was keeping me motivated to go to class because I was enthralled with all things aviation (still am 25 years later....) However, I was blessed with good timing, a steady Air Force job, and a job at a (for now) stable airline.
The corollary to this for military guys is that every bit of additional training you can get is valuable too. Like every other fighter pilot, I wanted to work in weapons, then in weapons, then in weapons. When I got to Tyndall AFB after being an Ops IP and Flight Commander I knew I was headed for an OSS job. Instead, I took a side track into the Med Group to become an aerospace physiologist. That led to me being selected to develop the wing CRM program. That program led to me becoming the SME when we got contractors to come in take over and develop a program. Those same contractors were...guess what...FedEx pilots. The skills I learned outside my primary loves shooting, killing, and blowing stuff up really helped me make some solid airline contacts. It also gave me a lot of new skills--like classroom teaching--which later morphed into some of the work I've done since leaving active duty. I've had other friends take sideline projects in computers, sim training setups, or fighter beddown projects (F22) that all led to having great job opportunities on the outside when these guys were done.
These days, I am also doing some work helping some DOD folks find the right guys for contracting jobs. Guess what the first question I get asked is? What is that person's security clearance and is it current? In short--the higher the clearance, the higher the paycheck.
Point to all of this? The more you know--the more diverse and wide your background is--the more opportunities you are likely to have in front of you. We all aspire to be successful pilots, but having a plan B, C, and D can sure help you sleep easier at night. There aren't any "bad" qualifications to have, and the more you can offer a potential employer the more likely I think you are to have a shot at whatever is out there.