The Nagant is stronger (though yeah, that's not really needed), and far cheaper to make. The latter is why only cavalry got the 3. I'm fairly sure S&W ran into the same problems as Remington in that the russians couldn't always pay them, too. Nagants are a pain in the ass to load when you're standing still on solid ground.
It's one of the few guns I've owned and gotten rid of with absolutely no regrets.