Unfortunately, none of the solutions worked for me. iPhone 5 with Mavericks and iTunes 11.1.2 (31).
Tried installing an app...delete the app...both install and removal processes and it will still get stuck FINISHING SYNC. Tried changing something via iPhoto, download and delete photos and no success.
I clicked the eject button beside the device icon on the left pane and iTunes did not really complain that a process is still in progress...THAT I found odd and it still ejected my device. Unplug device and reconnect...still got stuck finishing sync.
I'm actually starting to wonder if the process actually finished and just the graphic and status window above is just not resetting to the finsihed/ apple logo. My 2¢.