No contest as to which is the "better" action/rifle.
The pre/early war mausers were absolute works of gunmaker art. Actions that were practically hand-fitted, no machine marks visible, smooth, SMOOTH actions, deep lustrous bluing... just beautiful. And they were BATTLE rifles. Positive controlled feeding, extraction and firing. Solid action, not a split rear ring.
I'm not that familiar with the "K" version, but the overall design is just head and shoulders above the Mosin.
.... and I LIKE the Mosin. But, as stated before, it was more of a "peasant-proof" design. It functioned well, but had some design compromises.