I think it's because of the talent behind the songs, and the lyrics. Some movies use iconic music like Tchaikovsky's. He made some of the most popular themes in all of classical music. They also have award-winning composers like Arnie Roth. Other times, they use teams of writers who have worked together before and can come together and make great songs (The Rock 'n Royals soundtrack).
There are also beats that make you want to sing and dance. You could listen to the Barbie as Rapunzel music to relax, and the Princess & the Popstar music if you want to party! If you want something funny, listen to The Rat Song from Barbie as the Island Princess. Music for Christmas? Listen to the Perfect Christmas and Christmas Carol soundtracks. Then there's the lyrics. There are inspiring songs like "I'm On My Way", "Only A Breath Away" and "Making My Way". There's probably a Barbie song to suit every mood, and I think that's why they're melodious and touching.