By the end of the war the Soviets had much better weapons than the Mosin available. They deployed millions of SMGs. meanwhile the Wehrmacht was still mostly using Kar98s and equivalent bolt action rifles.
Nazis did tend to use the Mosin but looking into it, it's probably more due to availability of ammo and the fact that they didn't freeze shut like German rifles did
The one's who got the better made Mosins (especially Finnish ones) really did prefer it. But of course the wartime pressures on the Soviet economy made quality vary widely. (that's what happens when you move your factory half way across the country and try to make stuff with completely different steel.)