I was having the same syncing problem with my 4S, iTunes 11.1.2 and iOS 7.0.3. Time after time, it would hang up during the "Finishing Sync" process. No new music would be added, nor would playlists be updated.
I went to the Music tab and unchecked "Sync Music." When I did, I got the warning asking me if I wanted all music to be removed from the device. I said yes and did another sync. After doing so, it still was getting hung (although the sync button became active again), and there were still a couple of playlists and songs left on the device (as well as an audiobook). I went to the Books tab and unchecked "Sync Audiobooks" and clicked "Apply." After the sync, once again it was hanging and the sync button became active.
Here's what I think helped: On the iPhone, I deleted the remaining playlists and songs by swiping over them (just as you would delete an email). From then on, when doing a sync, it didn't get hung anymore...Completed the sync process very quickly.
I then re-checked "Sync Music" and "Sync Audiobooks" on their respective tabs and re-selected the playlists and music that I wanted to sync, and everything synched as normal. All new music was added and playlists were updated upon re-uploading.