There's another thread discussing AA's prices being higher for domestic flights. The price differentials for economy fares between AA and other major US carriers are even starker for transoceanic flights.

I'm seriously wondering why I should keep flying with AA.

After being primarily a DL Skymiles customer for 7+ years, I moved from NYC to MIA and began shifting to AAdvantage over the past couple of years to take advantage of MIA being an AA hub. (I was annoyed, for instance, that it was often difficult to find nonstop MIA-LAX flights on DL while there were usually plenty on AA.)

I fly mostly to Asia and Europe, typically purchasing flights less than 3 weeks prior to departure. I've found that AA lowest published economy fares are almost always several hundred dollars higher than UA's, and are often higher than DL's as well.

This summer, the differences were often as much as $1,000 more for travel commencing within 1 - 2 weeks of ticketing. But the prices have remained high even as we move into fall.

So my question is:
What are the specific advantages of the AAdvantage program that merit my sticking with AA?