Depends on UA's plane. If you get the new flat bed, that's preferable. If not, then i'd go for AA. I think UAs 767 are all converted, but the 777 are still being converted (or vica-versa, check UA forum for details).

I'd be very suprised if you cannot pick the flight to be sure you get the flat bed.

I'd take BA or VS if available, though.

Shawn