The 'Carbone' is easier to grind, using simpler tools, therefore easier to make thin & sharp. If one takes the time to make an Inox version as thin as the 'Carbone', it'll slice just as well, and maybe even better. I say this, because the Sandvik 12C27Mod stainless in the Inox version seems to retain some very, very fine 'tooth', even when polished to a fairly high degree. Combine that with really thin geometry at, and behind the edge, and it becomes a vicious, slicing BEAST. The carbone version will be nicely shaving sharp at the same degree of polish, but doesn't retain as much of that micro-toothy bite, taken as far.
Also, the Inox seems to be a little more durable at the edge than the 'Carbone', when both are taken equally thinner. I purchased one of each a few years ago, and thinned the blades on both of them. I noticed the carbone version tended to be more vulnerable to impacts & dings at the edge, after doing so. The Inox has held up better, at essentially the same geometry.
So, for light chores around the house, the 'Carbone' is usually the one I reach for. But, if doing something a little more wearing on the edge, like chopping fruits/veggies on a cutting board, I'd likely prefer the Inox. Not to mention, for food use, the Inox obviously won't impact the taste or smell of the food at all, like the 'Carbone' can do.
They're cheap; so it's not unreasonable to get one of each.
David