You will not be able to use a factory unlocked or AT&T iPhone on Verizon. Here's the official word directly from Apple's website:
"The unlocked iPhone includes all the features of iPhone but without a contract commitment. You can activate and use it on the supported GSM wireless network of your choice, such as AT&T in the United States.* The unlocked iPhone 4 or iPhone 4S will not work with CDMA-based carriers such as Verizon Wireless or Sprint."