Sorry, but NM and AZ do not have nearly identical weather. The entire SW half of AZ, including Phoenix and all its vast and populous stretch, is MUCH HOTTER IN SUMMER THAN ANY PART OF NEW MEXICO...
In fact, except for the Las-Cruces-El Paso region in the S Central area, not much of New Mexico is really hot in summer at all.
And only one or two towns in AZ, like Flagstaff, are cold in winter like the whole N half of N Mex is.
And, surprisingly, average rainfall in New Mex if anything is LOWER than that in AZ.
If you track across lattitudinal lines the weather is nearly the same, I've lived in both. Most of NM cities are in a higher altitude so you get a ver slight reduction in temperature. What makes NM seem cooler is that most of the cities are further north than their AZ equivalent. I've done parts of July in both Yuma and Roswell, good God it's hot (I say this as a person who's spent most of his life in the desert, Yuma and Roswell go beyond mere desert hot). The whole northern half of AZ get's plenty cold, problem is there's nothing inbetween Phoenix and Flag (it's a visciously mountainous region, not a lot of room for cities and such). Phoenix also has the additional burden of all that concrete, it should be cooler than Tucson, but it's hotter.