for the average, non-status passenger with no inclination to pay extra for premium seats or seat selection fees the BA A380 is best.
Very comfortable and quiet new plane, good IFE. 10-across seating is way nicer than in a 777 here.

The AA 777 will likely be a 777-300 - nice new plane with state-of-the-art inflight entertainment system and power, BUT sardine-like 3-4-3 seating in narrow and cramped seats.

BA 747 - old, loud and rattly. Here as well, terribly dated IFE and no power.
I avoid those if not seated in the upper deck or in row 1. BA is in the process of refurbishing those, but that's a long way from being completed.
Also, the 747 flight is the early departure, which is less than ideal as most people will struggle to fall asleep after meal service with their body clocks still set on Florida time.
The A380 flight and the two AA 777 flights are timed better with their evening departures.

One more aspect: If you don't finish your trip in LHR but connect to elsewhere on BA, it's preferable to fly BA instead of AA as AA lands in T3 and the BA connecting flight likely leaves from T5 - the terminal transfer from AA in T3 to BA in T5 is a pain, involving bus rides and long walks.

On BA, advance seat selection only free at check-in, so make sure to check in online right when that opens 24 hours before departure. Try and snag a seat on the upper deck for the best experience.