American Airways had always used the red and blue colors, along with an eagle, which they kept in their new design. The red and blue are obviously patriotic colors, and the addition of the white eagle improves the color scheme and makes it even more patriotic. The new logo incorporates an eagle into the shape of the wing of an airplane to add more motion, resulting in a logo that seems ready to take off.
One thing that I thought that could have been improved was that the new logo doesn't use anything from the logo from U.S. Airways, which was a blue (sometimes gray) rendition of an American flag with a tiny square in place of the stars. Although the former logo wasn't the most effective, the shape of the American flag was one way to provoke pathos in customers with "American pride", but that was sacrificed for the airplane/eagle shape. This new logo doesn't give an impression that the two companies merged but rather a feeling that American Airplanes has simply changed their logo like Google did recently.
The simplistic overall view of the logo seems to match the recent trend, which is to make logos and layouts as clean and simple as possible, instead of adding intricate details. The former American Airlines logo had a bit too much details on the eagle and U.S. Airways might have had too many stripes relative to most of th logos that are updating. The new logo is more visually appealing to most viewers now and seems more elegant than tacky. Personally I like this logo better and think that the new company did a nice job.