I find FFD to be better, and although I love Credence, I don’t get that excited about the CCR at LHR. That said, to me the in-flight hard product is the most important factor for me, and I prefer BA, especially with the new suites. But I just flew AA last week, and it was fine, and had no problem accessing the CCR (although I suspect I would have preferred the buffet food in the F lounge than the disappointing burger in the CCR).
BTW, when transferring at LHR I always use the F Wing rather than flight connections to clear security. When I landed in T3 last week, I took the flight connections bus to T5, where I cleared immigration using the e-gates and went up to the F Wing on the departures level to clear security.