To answer your question about CX vs. AA: CX wins in basically every aspect in my opinion, even if you get the older herringbone style seats.
These older seats are a bit small, but go flat and are much better for sleeping. The new seats are significantly better. AA has sloping seats. Food and service is better on CX.
If you have a choice between AA and LAN: LAN
The only advantage AA has: upgrades to F.