>When you go to battle a friend, if you set the game up, you can also select Music.
To change the music, you have to battle with somebody registered on your friends list, you also have to be the person hosting the battle. If you haven't already, try registering both of your 3DSes to their friends list and have a battle between the two. The hosting 3DS should be able to change the music, unless you're battling between ORAS and X/Y, in that case, it will only play the X/Y trainer battle music.
Hope this helps!
Sources: This and this.