Bristol's catchment will spread as far as afluent towns such as Newbury and Bath to the east, Cheltenham to the north, the whole southwestern peninsula and of course Wales which with the slow decline of CWL now has BRS as its principal departure point. Of course all these areas also have their less well of areas, but if you just take house prices as a (rather poor) yardstick many are way more wealthy than Birmingham, Coventry. Sandwell, Stoke etc. More wealth generally means greater disposable income.
BHX is really not doing too badly, probably at least as well as could be expected, though without doubt not as well as most would wish.