They didn't break up the Dixie Chicks. Natalie didn't feel like going into the studio and the other 2 did so they just took another name. The Chicks reunited to tour with The Eagles but that flopped and most of their shows got canceled due to poor ticket sales. They placed most of the blame for that on The Eagles for trying to sell high-priced tickets in a down concert market but I'm sure having an unpopular supporting act didn't help their cause.
The Eagles are more dope smoking idiots. Frey and Henley are big libs. Their music su*ks big time. Earwash.