I would think if you could afford the AA F, you could afford to buy a set of headphones.

I really enjoyed BA F product. I would find the daytime flight to be much much better. IMO the food, the wine and service are excellent. Also when you land you get to use the Molton Brown Spa - very nice idea BA. Nothing like getting off of a long flight, having a long shower and half hour massage.

As far as sleep goes, if you can afford a F flight, I am sure you could afford a hotel. I always sleep better in any hotel then I do in a F seat. BUT, I do find the F seats on BA to be pretty good beds, and do sleep fairly well. The down duvee and full size pillow are a plus.