I have a 4S that is running iOS 7.0.3. When connected to the Mac two things fail to happen:
1 - iTunes doesn't launch and I have to manually do so
2 - The Sync is stuck in "Finish Sync" and the only way out without quitting iTunes is to tell the app to run a backup
Open iTunes when press Command , (comma) to open iTunes preferences then select the Devices tab.
Deselect: Prevent iPods, IPhone, and iPads from syncing automatically
Reset your iPhone.
Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.
Then try syncing.