Two airlines stood out in the annual report on service.
United improved its performance in all four categories. While that is certainly encouraging for United travelers, Headley says the airline had plenty of room for improvement.
"They had a horrible complaint rating a year ago and they really had nowhere to go but up," he said.
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By comparison, Southwest, which is in the midst of completing its merger with AirTran, saw its performance drop across the board. Headley said that could be a sign Southwest is struggling with growing pains.
"Many people always prefer Southwest Airlines, but yet their system is getting a lot more complex," he said. "They are adding a lot of routes, they are growing, and we all know that is a difficult job in today's environment."
Overall, the industry has come a long way from 2007 when the AQR recorded its lowest scores.
—By CNBC's Phil LeBeau.