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Amish are literally pacifist. Mormons aren't. I've never even saw an Anabaptist who owns a gun, they slaughter animals old style, sharp knife.
I doubt assault rifles are acceptable technology for the Amish too.
I wouldn't put it past the Mormon army to use nukes, but I doubt they need to, and the population density of Amish isn't going to give us the megadeaths we want from nukes anyway
My money's still on the Mormons in a conventional fight, especially as the Amish (as you said) are opposed to fighting anyway
The Mormons even have a nascent arms industry. A bunch of up and coming gun and silencer companies come out of Utah and Idaho.
Finally, the Mormon church has literally 100 billion dollars, impassable mountains with simple chokepoints, trained veterans with combat experience, and zero issues with using the latest technologies.