New mexico was most valuable to both the union and the confederacy because

It provided trade access to the west coast and Mexico.

Explanation:

The New Mexico Territory included the modern states of New Mexico and Arizona as well as the south of Nevada. Both Confederate and Union authorities alleged ownership over the territory, and many major battles took place there, because it was key in the Trans-Mississippi Theater of the American Civil War, as well as a trade access point to the west coast and Mexico.

History tells us that it was a group of Irish men who were the last to fight for Mexico in the Mexican-American war. For people in the United States, “Los San Patricios” are considered traitors and guilty of the highest crime one can commit, treason.