When US Air and AA merged several years back, they had to reconcile 2 unique Co-Branded Credit Card Contracts.

What it boiled down to was that Citi could advertise online, specifically during the ticket purchase process on AA.com, and in the Admirals Club's system wide. Which made sense due to Citi issuing the AA Exec card.

Barclays got the rights to advertise in the rest of the airport areas, and onboard, including the somewhat laughably misleading credit card pitches from FA's. The FA's do get a form of commission for any approved applications.

(My favorite one - "With the 60K miles you get from this card, you can take your entire family to Europe, maybe even in First class!" ... where do I get that award chart!?!?!)

As far as which one is better?

I prefer Citi: Better bonus categories for everyday spend + periodic bonus promotions. Plus, the CitiGold Checking Combo can be a nice double play as well (offset some of my Exec fee this past year). Customer service is better too.

Barclays is a bit more stingy with bonus categories and promotions. But, they offer good balance transfer promos if you have a need for that type of financial service.

Both were able to churn for miles for a while until AA cracked down on new applications and that whole rigamarole a while back.

And yes, totally ok to hold both a Citi and Barclays card tied to your single AA account. (During the "good times", I had 12 different AA credit cards between the two brands at one time )


Edit to add:
If you have high enough organic spending (or can MS comfortably these days.....), and have a need for extra EQM/EQD - the combo of AA Exec + Aviator Silver get yous 20K EQM and 3K EQD yearly with $90K combined spending between the two. Annual fees of $694 for an AC membership, $25 per calendar day food and beverage credit on-board (I milked that one for a while, pre-COVID), $50 annual WIFI credit, and 3mi/$ on AA spending. It isn't THE best combo out there, but if you are loyal (or captive) to AA - it is one way to make the most of it if you are into the CC game.