I"m EXP on AA and yet fly 4-5 times a year on CX to HKG from LAX.

CX wins

Food
Looks of FA
Lounge
In-flight Entertainment
B and F class overall experience
Free booze on flight

AA wins

FF program
one might not earn AA miles on certain CX code
About an extra inch of leg room
A little bigger seat pocket, and the areas where your knee hits is cushioned, which on CX is a plastic shell (again more leg room)
Seats recline more