Much like the finishing JNats themselves, I think it really depends on the individual piece. I have used Koma that are very soft and seem a slight bit coarser and Koma that are very hard, which seem to cut finer. I think ideally I would try to match the Koma hardness with the finishing stone, but that's not always easy to do, and most sellers that I've seen don't rate Asano nagura hardness - but you can ask.

I don't think that Koma will ever be a step past a good Tomo though.