When choosing abrasives, the CBN vs diamond decision usually comes down to the work material. Diamond works best on non-ferrous hard materials like ceramics, glass, and carbides, while CBN holds up better on hardened steels due to its thermal stability.
This comparison breaks it down clearly:
https://ukam.com/diamond-vs-cbn-cubic-boron-nitride-tools/
I have zero knowledge about the polishing of anything except gemstones and glass. My personal opinion backed up by experience of many years is oxides work the best on most stones and glass below a hardness level of 7.5 to 8. Not including 8. If I’m cutting a competition stone 8 or above in hardness I use diamond at a minimum of 100k and depending on the stone may give it a final kiss with an oxide to make it just a tiny bit better. The oxides seem to peter out when you get past 7.5 to 8 in hardness for a polish but still seem to add a little something after the 100k diamond polish. I am completely ignorant of cbn polishes and metal polishing.