The American Southwest is a vast, ill-defined area, ranging from northern New Mexico to the border with Mexico and from somewhere west of the Colorado River to, perhaps, the Pecos River in west Texas. It's a diverse region with major human settlements located at elevations as high as 7000 feet and as low as sea level.
Architecture responds to place, that is to climate, geology, culture and availability of materials.
Therefore, in an area as diverse as the Southwest it stands to reason that its architecture will also be varied in form and structure. Also, to consider the architecture of the American Southwest independent of that of northwest Mexico would be neglecting a significant connection if not a crucial source of development. After all, the native cultures were linked by trade, and the earliest European settlers came from Mexico. Needless to state, the border between both the US and Mexico is a political line neither respected by natural history or biology. Natural determines, such as climate and flora that help shape architecture are not confined by any such construct as a political border.