Guessing not all chromium oxide is the same. Some 0.5 micron - good for final polishing after honing progression. Some more abrasive maybe 2000 grit - good for refreshing edge when it starts to tug after use. Not sure where to buy the stuff and be sure that I get one of each.
I use finer green pastes. There are two different eBay vendors in the UK selling 0.3 and 0.5 respectively. I guess we only have their word for it but I've tried both and they work well between stone and strop.
I have in the past used the heavier cutting compound from dialux but not these days - find it better to use a stone.