First-Despite the Flagship Suite, BA
's first class is superior. It is constantly acclaimed and BA
knows how to deal with First class passengers better than anyone.
Biz-BA's flat beds beat anything on a red-eye that is well...not flat.
Coach-I will go AA
on this one. With only 3 classes in comparison to 4 you get treated better because you're 3rd tier, not 4th tier. MRTC makes the decision even easier.
It all depends on where on the plane you're flying.
Have a nice trip