I spent 10 years at Eagle and I currently work for Delta. I know the AA system very well and have sat on my fair share of AA jumpeats as well as just know their overall gist at AA. I think their an amazing company and one which I would also love to be with. That said Delta hired me first and I live in a base that has both for a HUB( just lucky where I live). Having spent some time at Delta I am incredibly honored to be here, but in all reality no more than I would have been to be at AA. I spent years commuting and that is the most debilitating endeavor to go through on a continuous basis. I personally believe that both companies will provide you lots of upwards mobility, pay, and all the other incentives you seek in your life.
I personally would chose the company that will allow me to NOT commute or if you chose to live in a location that isn't a base one that provides you the best commute opportunities ( commuting on a mainline and not relying on a regional lift) I hope that gives you a little help, and congrats!