Verizon is the best despite rootmetrics potentially unfair measurement system. 

Statewide for Arizona AT&T actually came out ahead of Verizon (at times), in Tucson Verizon is ahead of AT&T. 

The reason that AT&T comes out ahead though is because of how the two networks are compared.  Their testing measures the strength or speed where they have coverage and where AT&T has coverage overall their strength or speeds are better than Verizon, however it doesn't take into account the areas where Verizon has coverage and AT&T doesn't.  So if AT&T covered 40% of the state and Verizon 80%, but AT&T was stronger in that 40% then they get a higher score (these numbers are not realistic just for arguments sake).