Ralph posts about refurbishing, I post about stones and sharpening. Ralph's are at least interesting, I expect mine not so much. Everyone it seems has their own way of sharpening and never should other ways intrude.
I also have sharpening round heels. C.S. posts that sharpening should be like a marriage, one system for life, As I said I have round heels, I not sure if I'm a cad or a slut but whatever I like different types of stones, but I'll pass on sandpaper and films. The different types of stones all lead to the same place but get there in slightly different ways.
The greatest differences are in the feel of the steel on the stone and the amount of monkey motion needed to use. There is not much need to revisit oil vs. water, it has been beat to death. The only thing I'll add is neither is quicker than the other, with oil stones you spend a little more time with steel on the stone. With most water stones you spend more time working on the stone. It is usually a wash.
JNat stones will kinda fall in the middle, they are slower than man made waterstones but faster than oil stones and their maintenance needs tend to be between as well. What JNats bring to the table is better "feel", better feedback as to what the steel and stone are doing. I know all touchy feely and unable to quantify but it is there. The other advantage of JNats is the grit can break down in the sury and as the steel and stone work together you can have a fast stone give a nice finish.
Posting about the finish of natural stones, oil or JNat, is where you can call B.S. but I prefer natural over man made. A man made stone like a Shapton will give an incredible shine but when you look through a lope you will see many small scratches lined up. Most JNats will not and no Ark stone will give that mirror shine in fact when you look with a lope the surface appears almost matt like when using either type stone with a very random scratch pattern. The shine looks great but I think the matt is a very slightly better working edge.
Here are four chisel sharpened with different techniques. You can't see the differences in the photo but I can tell you about them.
The chisel on the left is a #1 White Steel sharpened on JNats with a flat bevel. The steel has a "smokey" appearance with a well defined intersection between the steel and the backing iron and a fine matt finish when looked at with a lope. The next chisel is a A.I. O1 with a grinder bevel and also sharpened on JNats. The cutting edge also has a very fine matt finish. The new production Stanley 750 was sharpened on oil stones. The finish stone was a Washita and the chisel was stropped on leather with green stuff. It has a hell of a shine and under a lope a very fine scratch pattern. The last chisel is another #1 White steel sharpened on Shapton man made waterstones. There is not much difference in the shine between it and the 750 but under a lope the scratch pattern is more defined. One of the other differences is the definition of the line between the steel and the backing iron is not well defined like it is on the chisel sharpened with JNats.
The real question is: Is there much difference when steel meets wood and the answer to that is nope.
All four chisels are very sharp, all four hold their edge as well as can be expected for the type of steel. The next question is do I have a preference and that answer is not much, The JNats give great pleasure when steel meets stone, The Shaptons are wickedly fast, The oil stones make it very hard to screw up an edge. Each type of stone will give a good working edge.