My persepective.
Do the Engineering degree. I did Mechanical Engineering as it was the most relevant subject to flying at my local University. Couple this with my PPL and some military experience in the TA; which I used to fund said degree, led to an Aerospace Engineering job with BAE Systems.
I ended up working at a large northern airfield; where I ended up talking to Test Pilots on a daily basis as part of my job. The company had it's own flying club and an internal corporate airline. As a result I have made many useful contacts that I would never have made had I took the other career path that I was offered (Police Officer).
I eventually found myself working on a large aircraft project while studying my ATPLs. The cross over was immense and helped greatly. I was in a permanent aviation mindset.
Ultimately, in a future interview with an airline what is easier to sell - that I was a Police Officer for the past five years or an Aerospace Engineer. The latter shows interest, relevant skills and a passion for aviation.
You'd be a fool to do Political Science.
