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The real question is whether you will be able to find low-tier award seats between NYC and Western Europe between Christmas and New Years. If you can, getting Citi/AA cards would be a better bet, as AA only charges 40,000 miles for a Coach roundtrip between October 15 and May 15. Just make sure that the award seats are not on BA flights: TATL redemptions on BA flights have steep fuel-type surcharges.

You'll be able to start checking award availability on aa.com and united.com for late December travel starting in early February. But award availability can change dramatically over time.

Aside from which card, be aware that you'll save some bucks by flying into England and out of France, because of the U.K. APD and PSC fees on flights that depart from the U.K. Taking the train from London to Paris can be a cost-effective option, especially if you can book the train trip several weeks in advance.