BA F - the ground experience at LHR is better (First Wing, Concorde Room - book them a massage through You First etc.); also at JFK Concorde Room is pretty nice. Onboard: food and drink will be better, and seat is comfortable and crews will spoil them if they know it's their first trip in First - BA much more fun in this scenario than AA.
AA for J (on the 77W, especially) but at the same price point I would say BA for F.