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Nagant is Russian, Mauser is German. Nagant is chambered in 7.62x54mmR, Mauser is chambered in 7.92x57mm Mauser. The Nagant has been more mass-produced than the Mauser.

Beyond that, I honestly have no clue. Both are bolt-action, both were developed before WWI and both were used in every war up till after WWII. Both are also good rifles.

In a mauser action, the bolt-head isn't removable from the bolt. In a Mosin, they're separate pieces.

The Finnish made Mosins up until the 70's, and their current sniper rifle is based on a Mosin action.

Well yeah, and Russia had the M81/59, but design of new Mosin-Nagants ended with the M44. The 81/59 was essentially an M38 with numbers ground off the sight to reflect reduced range. I had no idea the Finns had clung to the design, though. Tell me it at least has a bent bolt?

In related news, I swung by the gun shop today, and there was a PILE of M91/30's in the corner. I asked about pricing, and he said they were privately owned, and had recently been fire damaged beyond shooting usability. I was sad.