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For travel between Seattle and Europe, using AA miles will result in less out-of-pocket expense than using BA miles, as long as you do not use BA for the trans-Atlantic segment. AA does not impose fuel surcharges when you redeem its miles, unless you fly BA on the award.

Keep in mind that if you start your trip home from the U.K. (rather than from some other European country), you will also be charged the UK air-passenger duty (APD) and passenger service charge, which will add to the cost of using an award ticket.

If you can meet the spending requirements, you and your spouse might each be approved for two Citi/AA credit cards, and earn a total of 150,000 miles per person. The trick is to apply for both cards on the same day, one right after the other. One of you might wish to defer applying until after the other has met the spending requirements on the first set of cards.

BA miles can be used with minimal out-of-pocket expense for domestic travel (including to Hawaii and Alaska) on BA partner carriers AS and AA, as well as to the Caribbean and South America on AA.

Good luck!