iFixit has revealed in its recent teardown of the Verizon iPhone 4 that the phone could have supported both GSM and CDMA networks. They know this because the phone contains a Qualcomm MDM6600 chip which supports "HSPA+ data rates of up to 14.4 Mbps and CDMA2000® 1xEV-DO Rev. A/Rev. B." They also point out that the phone lacks a sim card slot which would be needed for it to support GSM networks.
Who knows why Apple did not allow the phone to actually support both networks, maybe Verizon didn't want it or maybe AT&T. Maybe the next iPhone 5 will support both Networks and be sold directly from Apple on a website where you can choose which carrier that you want.
Another difference with the new iPhone 4 than the previous AT&T one is the changed antenna design. As you can see above on the left is the Verizon iPhone 4 with 4 segments in the antenna design while AT&T on the right has 3. The changed antenna design allows the phone to work on Verizon's 2 800 MHz and 1900 MHz CDMA/EVDO bands, while AT&T had to support 4 GSM bands and 4 UTMS bands for international usage."Link to Original Source