This is an interesting thread, but difficult to answer because any natural stone, by nature, will be different from any other stone (even from the same mine). And then of course there's the skill of the person sharpening that comes into play (for example, I have a lot of experience sharpening my straight razors, but I'm still relatively new to sharpening kitchen knives). So it's interesting to think about, but not really useful. Experiments can very useful for yourself because they are with your specific stones and knives, but unless someone is going to buy those stones, the experiments don't (or shouldn't) mean a lot to them. But I'm a big fan of thought experiments, so here are my results:
I have a decent collection of razor quality stones (unfortunately, they're mostly razor size, as well), and I've tried to sharpen my knives on most of them, with varying degrees of success. With both razors and carbon steel knives, I start with synthetics finish on naturals. With stainless steel, I usually keep it simple and stick to synthetics (unless I feel like experimenting).
My current favourite knife finisher is a level 4 Nakayama that I originally bought for razors but didn't like the edges it gave - but for carbon knives, it's incredible (in my opinion). I find it's a little too fine for stainless steel, though.
I got good knife edges from a coticule I bought from Ardennes a few years ago. I found it was slightly too coarse to finish razors (maybe 6-8k), but I was happy with the knife edges. Unfortunately, it was a little too small to be comfortable to sharpen knives (6"x1.5"), so I sold it.
I know I tried sharpening knives on my BBW, but I honestly don't remember if I liked the results or not. The only BBW I have is on a natural coticule combo stone that's about 5"x1", so all I remember was that it was too small to be comfortable to use.
I tried a large (8"x3"), slightly coarser (~8k) thuringian slate hone, but found that it was too slow and too fine for knives. I have a couple of finer razor thuris (probably 10-12k), but didn't bother to try sharpening knives with those, I knew they would be way too fine and slow, and also too small (5"x1" and 6"x2").
I have a level 5 Aiiwatani that I haven't tried knives on yet, and probably won't. It's an amazing razor finisher, so I doubt it would be good for knives - I also want to keep it pristine. And I haven't tried my Arkansas stones yet - I just haven't gotten around to it, but I'm curious about the results.