After a couple months on the market, the first extensive surveys are in and guess what? The Verizon iPhone is showing higher consumer ratings than the AT&T version. The biggest difference, unsurprisingly, is coming through the dropped call percentage. While AT&T's for the iPhone is just under 5% of calls dropped, Verizon's is just over 1%. That's a tremendous difference since these are actually phones first and foremost. This is pretty much the overall difference between Verizon and AT&T in general though so it's nothing really to be surprised at but it does help public relations for the new Verizon iPhone after the AT&T version of the iPhone 4 was plagued by missed calls prompting many complaints from consumers.
However, overall satisfaction remains about equal as it is the same nuts and bolts product. Unless actually calling somebody is the main objective of your phone choice, and in this day and age it's probably not, there's really no reason to choose one or the other. It's not like one phone is markedly better constructed than the other. It's just a choice between Verizon and AT&T. Personally I'd go with the rock solid service of Verizon, but that's just me.