It's more complicated than it seems at first. The start is a chart that compares grit ratings from one system to another using abrasive particle size, measured in microns, as the reference. This would seem to be all you need, but it's not. Still, it's a good start. Look at the sticky topics at the top of this forum and you'll find "The Grand Unified Grit Chart". This relates most of the major systems to each other using particle micron size.
If you do some reading here, you'll find lots of talk about this, so I'll keep it brief:
Particle shape seems to have a big effect. Diamonds for example, seem to have a pyramid type shape and their very pointy tops seem to make deep gouges in metal compared to particles the same size, but with more rounded type shapes. Particle hardness also seems to have an effect. Very hard abrasives (like diamonds) will cut very hard metal more easily than softer abrasives. Diamonds cut almost anything.
Then there's the issue of clogging, where the metal "swarf" that's cut from the blade can get caught in the matrix of the abrasive, making it less effective. With diamonds it's mostly not an issue. With water stones I don't think it's an issue as long as you keep the stone wet and flushed.
There are at least 3 more considerations I can think of, but this is already starting to get long winded so I'll stop here. Different abrasives cut differently. Knifenut here on the forums often tells people to NOT mix abrasives from different systems. I think it's because they cut metal in such different ways that it can be hard to figure out what scratches were left by what stones and whether you've removed some or all of the previous stone's left overs.
One of the reasons I love this hobby so much is how subtley complex these issues are.
Brian.