I would say for the cabin layout, BA.
For the food, soory, but it is AF: Menus have been elaborated by Alain Ducasse, the first chef to have 2 restaurants with the 3 "stars'' in the Michelin guide.
And of course, as Gordonroxburgh says, a fantastic selection of wines.
And at CDG, AF has the same type of VIP lounges, dedicated way through security, and special services.
My choice? CDG JFK with AF, and return JFK LHR with BA. And if you have to travel from LHR to Paris, why not try the Eurostar (High speed train crossing the Channel)
Ecoute les orgues, Elles jouent pour toi...C'est le requiem pour un con