As a flyer who spent many, many hours on America West and American Airlines flights, I see the current status as not quite as good as either of these airlines were in, say, 2005. At that arbitrary point, HP had cheery, regularly on-time service with a can-do attitude to many places from PHX and LAS. I enjoyed my flights on HP. Contemporaneously, AA had professional, on-time service to many international destinations and partnerships with many international airlines that made them the best of the American airlines in general, usually by a significant margin.
When HP saved the old US Airways and took on their name, the service consistency dipped noticeably. Flying a new US flight sometimes meant good service and a sense of urgency in service, and sometimes not. The addition of new international routes was nice, but flying through PHL was such a big step down in experience that it swiftly became the hub to avoid, worse even than ORD.
Prior to the AA-US merger, AA seemed to falter or lose confidence as a company. While still professional and wide-ranging, the pre-merger year was very directionless. Once the AA-US merger took place, the new direction wasn't always one that I would have chosen, but at least a goal or objective seemed to calm everyone. For whatever reason, however, AA did not retain their unquestioned leadership of the American airline space. There were other airlines that were more profitable, there were other airlines that had better service on certain routes, there were other airlines that could boast more of this or that.
And so it is today that I might take a JetBlue or an Alaska or even a Southwest flight on certain routes. AA doesn't command my allegiance as it or HP might have done a decade ago.