We always use BA, chiefly because
(a) we're used to it
(b) we often fly JFK-LHR on a red eye, in which case going thru Ireland is less fun (from memory, gives less time to sleep) and BA has seemed to be a little cheaper than AA when i've checked
(c) for the daytime LHR-JFK flight, food and IFE is sufficiently good even in WT (occasionally WT+) (and we usually take books)