Did you have them do it at the Verizon store using their black box?
Use Google Contacts Sync?
Back up the entirety of your old phone to your PC, then pick and choose what to transfer to new phone?
Verizon Backup?
Moto Migrate?
Moto Migrate also brings over your complete call logs
What about text messages? Do they transfer also? (Asking not only for Moto Migrate, but for other methods as well.)