There is the semi-secret Flagship Bridge lounge which does offer a small menu, including the burger + bollinger, to J/OWS/OWE pax.

BA is far better if sleep is your goal (assuming you get a decent seat). As others have mentioned, AA keeps the seatbelt sign on forever and will wake you up much earlier. Everything about that trip on BA is designed for maximum sleep on the flight.

If you are over 6"2 then again BA exit row 62A/K is a no-brainer for the extra legroom.