It depends on your program. If you want to play your background music only while using your program, you should use MediaPlayer. Otherwise you have to take care of the BackgroundAudioPlayer in any situation. Also this will annoy users, who also want to listen to their own music while using your application.
Otherwise, if your background music is the main purpose of the program, the user would like to start your music and switch to other programs. Then it keeps playing and you can control the music in the volume bar. That's why you have to create a background task for BackgroundAudioPlayer. The main application will stop in both ways when switching to other programs.
In short: game background music should never play after leaving the game (use MediaPlayer) - but I never want to watch my music player counting the time, while listening to my music library (use BackgroundAudioPlayer).