Verizon has a roaming agreement with Sprint. If you have Verizon (America's choice), you have Sprint. Verizon has the same arrangement with Alltel. The America's choice "network" is actually the sum total of all three networks (Verizon digital and analog, Alltel digital and analog, and Sprint PCS), which is why America's choice covers so much more area on the map.
The only problems I've noticed with Verizon is that some people are confused about when they will or won't be charged for roaming (a newer ERI-Enhanced Roaming Indicator-phone that tells you with the text banner lessens the confusion) and when you're zooming down the road and the phone is switching to different networks, your phone may be off the air for a few seconds to someone trying to call you while the phone registers itself on the non-Verizon system.