Case's stainless will burr a little more than their carbon/CV blades. And Case has mentioned on their own forum that their stainless was hardened a couple points lower than their CV steel. The spec'd hardness for their stainless is HRC 55-57 - so that would imply their CV blades were likely in the HRC 57-59 range of hardness.
That being said, neither steel has much abrasion resistance in the form of very hard carbides. This means either of them will easily grind on most any type of sharpening media, be it natural (Arkansas) stones, aluminum oxide, SiC, diamond, etc. I've REALLY liked how both steels respond to a Fine India stone (used with oil). Incidentally, I also favor the Fine India for Buck's blades in 420HC. Both grind & hone easily on that stone, with the only noticeable difference being that Buck's slightly harder blades will be easier to clean up of burrs. But both of them are simple anyway.
I think Case's stainless takes and holds a relatively toothy edge better (as left by the ~ 400-grit India) than it will hold a highly polished edge. The apex gets kind of fragile when taken very high in finish. Their CV blades will do somewhat better at high finish than the stainless will.
As to the thinness of Case's stainless edges, I've been impressed with the thin grinds on their '75 pattern stockman. That's my favorite Case pattern and I have several of them - all but one of them in their stainless steel, which is just fine in that pattern. On the '75 stockman, the sheepfoot blade's grind is the thinnest I've seen on any production traditional pattern, from any maker.
