I have four different sharpening kits: Oil stone, Water stone, Strop, and EP (Chosera). With the exception of a few of my knives which don't sharpen well on oil stones, I seldom choose one or the other because it's "better." The selection is based on amusement more often than not. Some purposes call for a coarser edge than others, some knives won't hold a high polish long enough to make it worthwhile.
I don't know about you, but a lot of my stones weren't first choices but "just happened." They came along when there was a need at a good price, and voila!
Knives are not razors. You're going to have to learn and unlearn a few things. Fortunately, the most important skill, knowing what sharp is, transfers beautifully.
Oils stone -- Hall's Surgical Black Arkansas, my finest oil stone, for almost everything. I think I might buy a translucent Ark this year.
Water stone -- Naniwa SS 8K, or Chosera 3K. I've used a Naniwa SS for a long time. The stone is a lot of trouble and there are quite a few now on the market which are better. This last one is worn out, and I'll be replacing it with something from Japanese Knife Imports -- probably the Gesshin. The Chosera 3K is a good stone, but is too expensive for what it does.
Stropping compounds -- I usually strop on balsa loaded with compounds, then finish with un-charged leather. My coarsest compound is 1u boron, which is actually a fairly versatile finish. My next finer is 0.5u chromium oxide. I used to use and like CrO, so bought more when I got this new strop kit; but I don't like it anymore. Too shiny and smooth for kitchen work. I also have 0.25u diamond which makes for a well polished edge with enough tooth to be efficient. But honestly it's not just overkill, it's silly overkill. I'll use it on both my carving knives for Thanksgiving but only because I'm a nerd.
EP Chosera -- The 3K and 5K stones cover most of the finish bases. The 5K is quite good as a final finish. The 10K is a lot like a Naniwa SS 8K. It's more finish than you need, but whatthehell.
What else? I think a coticule edge doesn't work well in the kitchen. There's something about that finish which allows it to cut hair very easily but not flesh. Like CrO, probably not toothy enough. No experience with the Thuringian, so no comment either beyond that I hear it's more for razors than knives as well. Which J-Nat?
There are a lot of really good finishing stones. Your best choices depend on what you want, and how much you're willing to spend.
Edited by boar_d_laze - 11/20/11 at 9:41am