Birmingham is less prone to delays than Heathrow and security will typically be very quiet. On the flip side, you may be able to get a nonstop flight from Heathrow whereas there are no flights from B'ham to China.

However I'd be guided by exactly where in the Cotswolds you intend to go before making a call on this. Transport through the region isn't exactly fantastic but I live in that part of the world (and face the BHX/LHR trade off myself) so if you give more details I'll help all I can.

All things being equal, my preferred choice is BHX.