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.

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the confederate at bull run