440C has higher carbon content than 420HC (essentially double), though roughly similar to 1095, and much higher chromium content than either of those two. In addition to the corrosion-resistance afforded by some of the chromium, the extra carbon + extra chromium accounts for a greater carbide content (chromium carbide, specifically) in 440C, which makes it more abrasion-resistant. That also means it's a bit harder to sharpen by conventional means, like natural (Arkansas) stones in particular. It will respond very nicely to diamond and silicon carbide, and should also do alright on aluminum oxide.
420HC is sort of a 'middle ground' steel in between 440C and 1095, in terms of ease of sharpening. Lesser carbon content, and just enough chromium to make it stainless, but not significantly tougher to sharpen. Less carbon than 1095 (about half), which means it might not hold an edge as well as 1095 (carbon is what primarily accounts for edge-holding, in addition to decent heat treat). The lower carbon and presence of chromium also lends itself (usually) to making the steel a little more ductile, especially at lower hardness values. That ductility tends to make for some more stubborn burrs on the edge, which won't break off as easily.
1095 is the easiest to sharpen, because it has nothing in it to make hard carbides (like vanadium or chromium, or other alloying elements). Obviously, the lack of any chromium also means this steel has no corrosion-resistance as well. The lack of carbides also simplifies the grain of the steel, so it tends to be very fine (carbides are usually larger & bulkier). Finer grain lends itself to extremely fine edges and great slicers.
So, to summarize:
If you're looking for better wear/abrasion-resistance and high corrosion resistance -> 440C
If you want ease of sharpening and very fine edges -> 1095
If you desire a good compromise between corrosion-resistance and ease of sharpening -> 420HC.
David