In my case I'll keep the Visa because it works. (The Amex has problems getting the double miles on AA purchases to work. I hope to eventualy get it resolved for the purchases I've arleady made, but it gives me no incentive to pick that card for AA purchases in the future.)

Please note that I'm talking about cards from the recent away7.citicards.com signup promo which include double miles on AA purchases for the first year. If you have a card from an earlier promo, this may not be a factor.

There may be other benefits to the Visa. Obviously one is closer to 100% acceptance. Another is that per some thread in this forum, the Visa may have always-primary rental collision coverage. (But I don't use this as a factor for myself because I've long had a Diners Club card with always-primary coverage.)