The Davy Knot I learned has one more twist, to finish the knot, through the loop at the hook end.
When using 6x limp tippet I find the Davey knot to be a smidgen harder to tie than the clinch knot. But the Davey Knot makes a smaller knot at the eye which may or may not be significant when using a size 22 - 26 midge. I have no way of establishing whether it matters or not .... other than my opinion. My opinion and a buck and a half may get you a cup of coffee.
In thicker tippets and/or stiffer tippet, I find the Davey Knot is a little easier to tie than the Clinch knot. Part of the reason for that is that I use the Orvis Knot a lot now a days which takes several of the hand movements one uses in forming the Davey Knot. http://www.orvis.com/...ets/files/index.html
I have tested the orvis knot to be stronger than either knot and still be a small knot when formed.
Lefty Kreh and Art Scheck say that the Clinch knot is one of the weakest knots one can tie. Even though I have not tested a lot of other knots from my personal testing I can believe they are correct. Having said that though. I do use either the the clinch knot a lot without problems in the mountain stream fishing I do. Especially on cold or windy days when fine tippets blow around and my hands are cold.
My testing of the Davey Knot vs the Clinch Knot indicates that it is about 6 of one half a dozen of the other for which one survives the test.
Here is the test I do (which you can do yourself) with some of my test results. http://www.westdenvertu.org/Documents/knottest.htm
disinfect your wading equipment. wash boat. disinfect livewells / sumps, wash ur dog