Ever hear of the Tkiv 85? It's a modern sniper's rifle, but uses old receivers. Very precise.
It's a Mosin-Nagant.
Made to the same quality (say, pre-WWII MN91/30 vs M98), the Mosin-Nagant will usually beat the Mauser in the accuracy/precision department if one can get past the MN's trigger.
Additionally, the MN is conscripted-peasant-proof, and dang near indestructible.
Sticky bolt is caused by cosmoline. Clean it out.
Either will shoot more precisely than the operator, but the precision edge does usually go the Mosin-Nagant (properly manufactured).
Reliability may go to the Mauser due to its large extractor claw and controlled-feed design. This is theoretical, however. The Mosin-Nagant is put together in such a way that the push-feed does not cause malfunctions.
Massage the trigger, wrap the barrel in oiled felt, change out the sights to something better, and proceed to outshoot modern sporter rifles.