Massage the trigger, wrap the barrel in oiled felt, change out the sights to something better, and proceed to outshoot modern sporter rifles.
Perhaps that's true, but put the same amount of effort into a Mauser (which is unnecessary, by the way) and you would probably get a corresponding improvement.
I believe the OP wanted to discuss the two rifles as they were put into service... not what they COULD become with lots of TLC.
Wrap the barrel in oiled felt? What??
Where do you even FIND oiled felt? How do you keep the oil from getting all over everything? What does it do? Do you wrap it tightly? Counter-clockwise? How often do you have to change the oil?
Seriously... still, hands down, the Mauser. AND, I'll still take my Mosin out nearly every time I go to the range. Along with my Swedish mauser deer rifle, and my 1909 Argentine mauser .35 Whelen elk rifle. Hopefully, someday, I'll even get to USE it on an elk