My user profile was not synching between my iPad and iPhone in Plants vs Zombies 2. I was eventually able to get it to sync by using iFunBox to copy the com.popcap.ios.PvZ2.plist file from /var/mobile/Applications/<PvZ2_folder_of_your_device>/Library/Preferences to my computer from my iPad and then copying it to the iPhone. The player ID codes in iOS > Settings > PvZ 2 should match on all devices.
The synchronization is not instantaneous. It seems to take a couple of minutes. I'm not sure if the synchronization only occurs while waiting on the main menu.
There is a thread about this problem here.
Update: This doesn't appear to work consistently.
