Have only flown CX, BA (both old and new) and AA (including new 77W version, as well as old version) in F. CX clearly the best. In fact, I'd rank it ahead of any other F I've flown (SQ, TG, LH, UA) except for SQ 380 suites. I agree with others that CX F meals are not superb. But aside from that, I love it.

Between BA and AA new F, it's a toss-up for me. I fully agree that AA F service can really be inconsistent, so a definite edge to BA in the soft product. Plus flying out of LHR you can access the nice Concorde room, which is solely for BA F passengers. OTOH, AA has roomier seats and a less crowded F cabin. Plus if two people are traveling together you can turn the two middle AA F seats so that they face each other, which is nice for dining. (You also can turn the seat to face the window if traveling alone and if you want to easily gaze out while working, FWIW.)