If we’re talking about “preservation” in the strict sense, Mexico has preserved far more Hispanic architecture than the US, if only for the fact of quantity.
The house on the left isn’t “preserved” Hispanic architecture but rather Spanish Colonial Revival architecture from the late 19th and early 20th century. It’s the faux pastiche of California post card hotel and resorts for wealthy northeasterners.
Beautiful, yes. But hardly historic in any real sense and quite soulless when compared to the viceregal core of any Mexican town from Zacatecas to Campeche.
The United States did a much better job preserving Hispanic architecture (left) than Mexico (right). It's very common to see Spanish-style homes with white exterior walls and tile roofs in the Southwest. Mexico's architecture only has box shapes and lacks historical character.