Adding on to the OP: The UA app is really good in general. They've invested in it, and it shows. Self-service (both during regular ops and IRROPS) almost always works well through the app, which saves having to see / call an agent (win-win for the customer and UA). I'm not saying AA doesn't have any of this, but UA is the leader in this space and I'd like to see AA (and every airline) get up to that level.
What I'd definitely like to see AA improve is the long-haul J seats, particularly replacement of the dreadful Safran/formerly Zodiac Concept D seats. I have no issue that some seats are backwards, but the anchoring causing you to feel every movement of the person in the seat behind/in front of you is a just unacceptably poor product that has caused me to book away for years. Since you can't know which whether or not you will get a plane with Concept D, I just avoid booking the fleets that have them.
The new 789 seats certainly look nice, but some retrofitting of the poor seats on the existing fleet would be good. (There was talk of the 772s getting a retrofit, at least before the oil price spike)