Backup
Music collections can be very large in size especially if you use a lossless format.
Each time you edit a tag or the player software writes something in a tag (replay gain, playcount, etc.) the whole file qualifies for backup as any write action will change the date last modified.
Rsync
Rsync works a bit different.
It checks which part of the file has changed, only the changed parts are transferred to the computer containing the copy.
In case of tagging, this is the header of the audio file only.
This is a very efficient way to backup music files from one computer to another over a network.
You can use it to do remote replication over the internet even if you don't have a fast connection.
Rsync is Linux.
As a NAS often runs Linux, it is probably on board.
If you want to sync to a remote location, you must enable port forwarding on both routers.
If you want to use it in Windows you need cygwin.
An easy alternative is to use DeltaCopy maintained by Synametrics Technologies
Synchronizing
Another option is to use synchronizing software.
Most of these apps can be configured to resolve all kind of conflicts.
These are the options offered by DirSync