Owned and shot many of each. I like them both, but my heart belongs to the clunky old Mosin. They have their own pros and cons. The biggest difference is in their distribution and history. The Mausers spanned the world, and were used everywhere from Argentina to Siam. Each nation had its own particular model--and I include our own Springfield '03 among them. The engineers at Mauser were constantly upgrading the design, which created further complexities. The net result is a complex mix of rifles with limited parts interchangeability between models and subtypes.
The Mosins, OTOH, were developed in Czarist Russia and remained in orbit around Russia and the USSR. Most subtypes came from Russia's neighbors, most notably the Finns and East European nations. Some captures made it to Austria and Turkey, and of course our own nation had its share, but these never became anything more than obscure remnants. Plus, the Mosins never had a Mauser-like sales team pushing them. Nor did anyone bother trying to improve on the basic system. It worked well enough. Even the Finns couldn't find a cost-effective way of making it better. Their limited efforts with the infamous M-27 "wings" were a notable failure. It's the old Russian proverb, "The best is the enemy of good enough." The upside is interchangeability of parts between models is excellent.
Both Mauser and Mosin actions are tough, though Mauser didn't have anything as tough as the '91 Mosin until the '98. Mosin actions get a bad rap for sticking because people fire horrific ammo out of old parts rifles from the bargain bin. But I've had more and worse jams by far out of old Mausers. When you use bad ammo and add poor bolt fit and headspace issues, the jams are going to happen with any action. A smooth Mosin is as fast as a smooth '98--though neither is as fast as a Swede.
The Mosin uses big, archaic rimmed cartridges. Only the Siamese Mauser does likewise. The advantage of this design is it tends to be more forgiving of headspace variations, but it also means rimlock is a threat. And it makes most stripper clips for the Mosin worse than useless, since even if they work they're likely to insert the cartridges with locked rims.