This is a far from straightforward question. The natural instinct is to assume that its the hard surface that stands wear and the soft that gives way but usually its the other way round. Thats why when you strip down an engine you will always find that the rubber lips seal has worn a groove in the much harder crankshaft.
As for the materials, austenitic stainlesss steel is soft unless hard worked to make things like dental instruments. Whats more the surface coating that makes it stainless needs air to maintain itself, so in circumstances where there is limited or no air, abrasion will quickly remove the protective skin formed by the chrome and surface rusting will take place. You might never see this as its wiped away by continued abrasion, but its a mechanism by which austenitic stainless steel wears.
There are more grades of stainless steel than of other alloyed steels but the sort which can be properly hardened and will withshand the sort of use being discussed are expensive and difficult to source. Hence the use of chrome plated and hardened carbon or alloy steel shafts. Or just chrome plated mild steel for the cheepos.
By the way, stainless steel was another discovery we gave to the world.
