To automatically download music purchased on one device to the other, go into Settings > Store, and turn on Music on the device you want to receive the music (or both for two way). This will only work for music that you purchase after you enable the settings.
It may take a bit, but the song should download in the background without you having to do anything else.
To get older music on your other device go to the iTunes app on that device, open the Purchased tab, select not on this device, search or browse, then download it.
I don't know of any way to have and sync the same playlists on both devices, except to set those playlists up in iTunes on the computer and sync them both from there. This make sense when you realize that each devices music library is independent of the other. In order to sync playlists between them you would need identical music libraries (at least for what's on the playlist). You couldn't just sync the playlist the rough the cloud, you'd have to control the entire music library syncing in the cloud for each device. That option is not available, at least not yet.