Seconding rsync. It can very easily only copy what has changed, even if in your case this is new files.
AFP being Apple File Protocol? If the NAS also allows SSH use that, otherwise rsync will happily copy files as long as you can mount the AFP volume on a Linux box. I've never done it, but I'd be very surprised if you can't mount the AFP volume in Linux
Finally, rsync is the quick fix:
Code:
rsync -arz /src /dest
Only thing to note is to pay attention of trialling slashes on the source and destination. If you leave off the traling slash, rsync will create the last folder of path in the destination, but if you include the trailing slash on the source, rsync will skip that folder and copy subfolders and files of that folder directly to the destination.