Although my formal education is in engineering, I don't think said background in it of itself gave me a leg up on the flying bit. Self-motivation, MS flight simulator and falcon 3.0 (remember those games in the 90s? lol) did much more to prepare me. Engineering did make it easier to pretty much waltz through any aircraft systems course the FAA or the USAF has ever required me to take. Same for the math, and I admit, I'm very average for an engineer as far as arithmetic is concerned. Pilot math is inherently round-off-error laden, which is why I love it. I can spit out a 20% off number as quick as the machine can spit out the right answer, and that's why I'm a big deal up there
Pilot math... It may be wrong, but it gets ya home like a champ!
Which is also why I would have been an average engineer. I didn't have a passion for it. Understood the concepts, had the boredom tolerance to go through the syllabus and even excel academically. Loved the theory, but the workplace and expected day to day duties depressed me. So what if my current occupation lowers my life expectancy (all that RF exposure can't possibly be good for me), die with your hair on fire and your boots on, or don't show at all.
The cubicle life and the "we haven't done anything really revolutionary since Apollo, so here's the 32 decimal place data mining babysitting of the same stuff we did for panel #345 on the 737, welcome to your job" shift in job duties from those of the golden days, kinda knocked the wind from my sails and cemented my desire to fly more.
As to TPS, I don't think that the AF actually considers that to be true (engineers make better pilots), it's that for TPS the role of a test pilot requires constant interaction with dedicated engineers, thus having an understanding of the thought process of engineers is essential for a test pilot to be able to communicate (and also possess the technical writing format knowledge that is useful to said engineers making design corrections) with that group of people. That's really the jist of the TPS requirement of an engineering or quant-based science degree.
I've met real sierra hotel sticks on both quant. and liberal art educated folks. So it doesn't give you an edge on the flying. Remember WWII? We put monkeys out of a farm in Iowa and these young men managed to do things in the sky we still try to inspire children with. Book knowledge doesn't translate in a "make it or break it" way to the mechanics of operating machinery; be airplanes, cranes, ground vehicles et al.