Part of the card decision depends on what airline(s) you fly, in order to maximize the miles or points earnings & usage. We first got Citibank AAdvantage cards back in the '80s because we live in a hub city. AA purchases earn double miles, all others are 1 for 1. All miles transfer directly to the AAdvantage program, so are independent of the card. We have been able to redeem far fewer miles for trips that would cost significantly more in dollars, so if you travel a lot, this is where a mileage program is better than cash back.
There are now some caveats for the Citi AA cards: Citi now charges 3% for every transaction outside the USA, so we no longer use these cards while traveling overseas. Citi charges an annual fee for AA cards with a high or no annual spending limit for miles, but this fee can pay for itself because using the card for an AA flight will allow 2 free checked bags per person & priority boarding.
Newer cards now earn miles or points that can be used for any airline, but you have to charge the trip first before you can redeem for a refund against it. However, this means you can shop for the best fares regardless of blackout dates or mileage flight availability. We prefer the Barclaycard Arrival Plus World Elite travel card, since it earns 2 miles for every purchase, not just travel, doesn't charge a foreign transaction fee, & has the embedded chip that so many foreign merchants require. We were able to get it with a 40K mile bonus for spending $3K within the first 90 days & the annual fee is waived the first year.
