One can always look to the industry that has had access to both high quality natural and synthetic stones for the longest time and see what they use. I am talking about the Japanese carpentry and woodworking trades and from what I've read, they only use synthetic stones up to around 2000 grit. From there on, they use natural stones. Now this could be due to some type of tradition or reverence for the past, but time is money and these people are professionals, so I assume they are going for a sharper blade,a longer lasting edge, or what just plain gives the best result. Having dug around the net, here is a quote from So Yamashita (www.japan-tool.com),
"Using natural stones will enable you to plane thinner (more sheen on the surface of the wood) and at the same time it will make the edge last longer. This has a good reason. The sharpening particles of the synthetic stones are even in their sizes, whereas the natural one's are not. Therefore blade sharpened by synthetic stone will have even height of serrated teeth, so once those teeth gets dull it stops cutting altogether, but... when the height is different... I think you see my point. It's like the shark's teeth. They don't break all at once.
Also, the natural stone sharpening has a hardening effect on the tip of the blade. This has been proven scientifically by the HRC testing machine, experiment done by renowned plane blacksmith Usui Kengo. The hardness was actually harder after being polished by a fine Nakayama stone. So you see, it's not just about the sharpness you are getting from natural stones. Once you use natural stones, it will be unthinkable not to finish with them."
This observation has also been observed by Alex Gilmore (www.thejapanblade.com) and explained in his article, "Sharp vs Shiny":
http://www.thejapanblade.com/sharpvsshiny.htm
I must say that this is a very interesting subject, and I believe that either medium will give the user an edge sharp enough that the quality of his work will be dependent entirely on his/her skill. Natural or synthetic, when you are literally splitting hairs... anything after that is just splitting hairs.