The iPhone “xxx” is synced with another iTunes libray on “xxx”. Do you want to erase this iPhone and sync with this iTunes Library?
An iPhone can be synced with only one iTunes library at a time. Erasing and syncing replaced the contents of this iPhone with the contents of this iTunes library.
This iTunes message is most common when trying to update an iPhone in iTunes where the iTunes library wasn’t synced originally. It’s annoying.
Rather than find your iTunes authorization ID (Which only works if your backup is not encrypted) to try and force sync – simply backup your device in the new itunes library. Then, in the same fashion – click “Erase and Sync” when prompted per above.
Your iPhone will sync with your new iTunes library AND it will re-install all apps WITH passwords. It should be as if you didn’t even notice the restore took place! iTunes 188.8.131.52 seems to have awesome backup and restore techniques now versus older versions.