Of the 3 major US legacy carriers, AA's is by far the worst. It's my preferred airline, but the app is inferior. The main thing (for me) is you can't book award tickets on the app. You can on UA and you can on DL. Beyond that, many functions in the app actually open the mobile site rather than working natively.
It has a ways to go to catch up. I keep assuming it's "in progress" ... hope so!