iTunes or iCloud - restores your imessages
Verizon Cloud - does not restore imessages
They will not transfer over. Only iTunes will transfer that over and you must use an encrypted/password protected backup to do it.
Actually a regular iTunes or icloud backup will transfer your imessages. You don't have to encrypt your back up.
iClouds is encrypted by default. I don't remember iTunes would back that up without it being protected. It could have changed or I misread the tool tips.
iTunes or iCloud - restores your imessages
Verizon Cloud - does not restore imessages