from my experience (i have not used the 4k) the HC is a tiny bit slower than the HR on all steels. maybe 25% or more.
It polishes above its rated grit. the 6k gives you a shine like an 8 or 10k or similar, and the same with the 8k HC it polishes above its stated grit, at the cost of speed.
Then they feel kinda weird in use compared to the regular HR and shapton pro. those 2 feels very consistent, but the HC stones feels like grabby yet at the same time slippery, its like someone took a sandpaper then embedded small 1mm particles of teflon randomly all over the stone. and you can really feel this effect when doing them back to back.
wear seems very low just as the HR. does not release any abrasive, or very very little. just as hard as the HR.
I did not notice that they did carbon or any other steel for that matter better or worse than the regular ones. theyre just a bit slower.
so why even get these? well you can have a 6k thats just a little slower than the regular 6k and but it polishes like an 8k or higher.