How to copy music content and playlists between iPods (Nano 5th Gen 16GB)?
Assuming I understand your question correctly, would a backup > restore process do what you want? 

More specifically, have you tried doing a full backup to iTunes of the first iPod and then restoring that to the other iPod? Basically, when you connect the second iPod to iTunes you can do a Restore from the full backup you just created from the first iPod. 

Once you've done the restore, the music may not be on your second iPod to start with, but then syncing it with iTunes should restore all the music/playlists you had previously downloaded to the first iPod.

NOTE: I'm also assuming that all the music, playlists, etc are stored in your iTunes library on your Mac.