The Verizon iPhone 4 does benefit from the lessons Apple learned with AT&T's iPhone 4. Rumors suggest that Apple is developing a next-generation iPhone with multi-band support for both types of networks, but for now an AT&T iPhone cannot be used on the Verizon network, or vice versa. AT&T uses GSM and Verizon offers CDMA. These two systems are not compatible.
Network technology dictates the primary difference between the two carriers. You cannot talk and surf on the Verizon network. With AT&T, you can simultaneously access the Internet while you are on a telephone call. Switch to Verizon and you will lose this capability.
Verizon's iPhone benefits from improvements to the antenna design. AT&T consumers suffered the brunt of the issue when the iPhone 4 was introduced, and Apple has re-engineered the antenna to address lingering concerns.
A new feature available on the Verizon iPhone is the Personal Hotspot. Multiple Android phones offer hotspot functionality, so it's not revolutionary. It allows you to connect other network devices to your iPhone and share its Internet connection wirelessly. Your Verizon iPhone 4 effectively becomes a Wi-Fi access point.
If you are looking for a mobile phone to take advantage of faster 4G or LTE networks, the iPhone 4 is not it. The Consumer Reports blog offers reasonable arguments to hold off until the next generation of hardware.