Airport, sorry I blinked on the way through
"I would concur that if travelling BHX-JFK, BHX is least of your problems. "
As a frequent premium long haul traveler I second some of OltonPete's remarks.
For me facilities in the airport at either end are not so important. The biggest feature is simply being near where you want your journey to start or end.
Minimizing time in transit is very important. That makes nonstops like BHX/JFK really valuable and far more important than the facilities at BHX.
What is different is when you *have* to connect. Then the airport you connect in can make a big difference to your journey.
I don't think a lot of premium passengers connect at BHX, so I don't think the facilities matter that much and the airport is perfectly adequate.
2 cents.