As many reviewers pointed out in reviewing the iPhone 4 from Verizon, although the hardware is almost identical, the major difference is the networks. Reviewers also noted that on the Verizon 3G network you can't use voice and 3G data at the same time.
AT&T's answer to their take on the difference is seen in a new commercial. It shows a man in a conference room talking on the speaker phone and making a reservation at the same time. Apple's official iPhone commercial shows two iPhones on the two networks doing the same functions to the tune of the Blue Danube.
The Verizon iPhone sold out for Verizon presale customers the day it went on sale. There will be some Verizon stores opening at midnight on February 10 for iPhone sales.