Speaking as an underemployed (not seriously rich) Gloucestershire resident, my first preference is I'm afraid Bristol, although both airports are equidistant. Second is Luton (not much further), then Heathrow.
As to a reason, I am generally travelling south or east, so going north to the airport seems counter-intuitive. I also see Birmingham as expensive for parking, and with fewer routes of interest to me than BRS/LTN.
I flew from BHX a few times some years ago, and had no real complaints. From here, Birmingham is a different world.....