Also, I realize it's not nonstop, but you can take AS to Vancouver and BA to London on AA miles.

SD1K: On Alaska Air, you can earn and redeem on American, British, Qantas, Cathay and Lan, but you only earn status miles on American and Lan.

If it were my decision, I would stick with AA. Getting emerald status with BA and AA shouldn't be appreciably different if youre flying paid J to Asia. Emerald on CX is a lot more difficult in general.

Purely from a mileage perspective, you will get more bang for your buck with AA. I am going to make an assumption that you are flying SEA-LAX-HKG in paid F/J and redeeming to London.

AA: Each trip to HKG would net you about 37500 miles with COS and status bonus. At that rate, you would be able to redeem a J ticket to London every 2.4 trips to Asia and an F ticket every 3.33 trips.

BA: Each trip to HKG would net you about 21000 miles with COS (no status bonus on CX). At that rate, you would be able to redeem a J ticket to London every 4.76 trips and an F ticket every 7.14 trips.

CX: Each trip to HKG would also net you about 21000 miles with COS (no status bonus). At that rate, you would be able to redeem a J ticket to London every 2.85 trips and an F ticket every 4.28 trips.

Although I realize these are crude estimates and don't take into account things like other flying, bonuses, etc., I think AA is the most generous of the three considering the earn/burn rate and the ease of getting status. But considering that Asiamiles allows you to use BA transatlantic and allows you to use a few extra carriers, I would consider Asiamiles before Exec Club if you decide not to go with AAdvantage.