Yes, AA has been there for me for last minute awards and seems to have availability for flights when others are lacking. What I have figured out is that AA has best promotions, ie. double miles or 5-10-15k to Europe, etc.
I also like the idea of BA Silver for transatlantic and possibly intra-European. What I was doing until recently was depositing my miles from BA transatlantic into my America West account until I had enough to use and close down my orphan miles there.
I have heard great things about CX service but also that they were "too efficient" as friend puts it instead of saying stingy on awards and miles earned. AA also has great awards on CX in Spring at great discounts.
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"Fly me to the moon and let me earn alot of miles."