From my perspective on what AA gets right as an EXP:

1. IRROPS support - AA has almost always found ways for me to get home or get where I am going when operations break down. This includes forcing positive space on full flights, protecting me on later flights, or confirmed changes on other flights.
2. Value for miles - Partner rewards (when available) are of great value, particularly in First/Business; last minute redemptions in Business on AA can be very good; value in economy award tickets booked in advance with the ability to cancel and redeposit without a fee. For example, I recently booked a ticket to AXA for 24,000 miles round-trip next spring in economy on a flight that costs over $1000 before taxes.
3. EXP line - recently have rarely had to wait on hold, and the service here is very good.
4. Newly renovated lounges are great (e.g., DCA and LGA) and lounge membership via credit card does not impose visit limitations (e.g. number of visits per year or only X hours in advance of a flight).
5. While elite upgrades have declined amongst all 3 majors due to monetization of first class, I am still have a very good domestic upgrade % and worse case I am in an extra legroom seat in economy. Complimentary upgrades to premium economy on international routes for myself and companions is also a fantastic benefit.