Why does it matter who operates it?
Well, despite what you think, there may be very different cost structures involved for a start. Just because both airlines operate a B788, does not mean it costs the same for each airline to operate it, not by a long shot.
Crew costs are different, maintence costs may be completely different, fuel prices may be different and so on. Usually, labour is the main cost difference, and labour costs in the US are usually higher on legacy long haul airlines, if it mattered, then why do you think Delta swapped out for Virgin on both Manchester routes, and did the same on a fair few LHR routes also? After all, with your reasoning, both VS and DL operate the A330, so no sensible reason that the costs are different, surely?
Lastly, reputation may be another reason. Most pax on AA originate in the Manchester end, and many people will have booked the flights via a BA source. It will therefore beBA having its name tarnished by the shoddy OTP too.