I'm late to this post, but I have a thought about this. I've been a regular stone pig of all types, partially due to woodworking and partially due to razoring. I've never seen a natural stone that is reputed to have particles regularly smaller than 3 microns.
The 16k range stones are slightly sub 1 micron.
With natural stones, you're hoping for a stone with a mostly closed matrix, particles as small as possible and the ability of the particles in the matrix to stay put and get dull.
There is a learning curve with all natural stones, especially if you're used to synthetic stones.
As a natural stone fanatic, there really hasn't been a synthetic stone I could get a great edge out of (great being keen and smooth) and I didn't have a synthetic stone that made what felt to me to be a more keen edge than a good japanese finisher. I think a lot of people who use synthetic stones more and natural stones less would disagree with that. I use natural stones more and synthetic stones less.
I'd hesitate to call a stone equivalent to a synthetic stone or powder because if you use the stone as the last step, the edge is going to feel different than a powder or paste edge. But the biggest variable in a natural stone that is:
* not scratchy / no toxic particles
* made of some kind of variant of silica for the abrasive (japanese stones, novaculite, jasper, hone slates, thuri, ...)
* hard enough to not release particles
* does not have any voids or even a generally open or partially open matrix
Then it's really up to the user.
I have felt like the hard japanese stones are a lateral move to a gok, but I like the edge off of a japanese stone better. It can be easily said that the japanese stone once settled in will cut slower, but that is OK, because your primary job with it will be maintenance, and maintenance requires an extremely small amount of metal removal.
With the fine stones, it's the learning curve that's the problem. it seems to me the best way to learn a stone is to force yourself to not use anything else at all for several months, and work your razor until you get an edge you like.
When we talk about which natural stones are like 16k and which are finer than 16k, it makes me cringe a little bit because none have particles as small as 1 micron or even close. It's the versatility of the stone and you as a user that makes the stones work well. Get an appropriate stone if you want and use it for a while. It may take many honings before it settles in to what you like. I know if I lap my japanese finishers with anything at all, even if it's just another stone, I don't like them for quite a while. I like them completely settled in.