Case IDs their 'CV' steel as basically 1095 with a little bit of chromium and vanadium added. Their 'Tru-Sharp' stainless has been 420HC.
They both are capable of taking equally fine edges all the way to hair-popping/hair-whittling sharpness, using the same methods and tools; anything from Arkansas stones and beyond, up to diamond hones. The biggest difference in sharpening them, is making sure the burrs are fully cleaned up on the stainless (Tru-Sharp) blades; they're a little more prone to holding onto burrs, and it takes a little more care & finesse to minimize them and remove them. A very light finishing touch on the hones to minimize and get rid of the largest portion of the burr, and some stropping on leather with green compound to clean up the rest, is what has worked well for me. Once finished up, they're almost indistinguishable from one another in typical non-abusive EDC uses. Not adequately removing the burrs is, I think, responsible for many of the negative opinions of Case's stainless blades, as the burrs left behind will fold quickly and leave the impression the edge has dulled much too easily. If the burrs are taken care of properly, the stainless holds up quite well as compared to the CV blades.
I've noticed most of the dulling on the edges of my Case knives is more related to abrasive wear (edge dulling or rounding by abrasion), and not edge-rolling or chipping. This means the potential difference in edge-holding between the two steels is less about RC hardness (which affects rolling/chipping behavior), and more about the lack of significant hard carbides, i.e., wear-resistance, in either of the steels. Neither of them are very wear-resistant, so that's why I view them almost identically in terms of how they perform in typical uses. I touch them both up with relatively equal frequency. They will wear; but, once the edge geometry has been set up in good form, either is extremely easy to resharpen and get along with.
David