Which airline loyalty rewards would you use between Delta and American?

Money board has a huge thread on this sort of thing. I recommend getting a Chase Sapphire though.

Sky pesos vs good award redemption, I'd go with AA. Which airline do you fly more?

if you have a somewhat consistent travel pattern that would probably be the determiner, as for using the mileage for personal travel, either of them go just about anywhere in the world you could think of

I prefer flying through Atlanta over Dallas but if American gives you more options I'd be inclined to look at the programs. Pretty sure all of them are close to the same, though. I'd consider a hotel or airline credit card as well. Or a venture card or whatever.