You could check the Knot Wars on North American Fisherman, they test them all on a machine. It's knot a fly site, but they do test mono, flouro, braid, whatever. My go to knot is the improved figure 8, strong, easy, joins unequal tippets, and does not waste material. I have also been using the palomar, non-slip loop, San Diego jam, and the Korean boat knot. milt. The figure 8 is aka the Orvis.
Like Casey, I personally find the clinch to be a stronger knot than the improved clinch.
When you make an "improvement" to a knot there's more of a chance that it will not draw tight. And knots that aren't tight will slip. And knots that slip will break.
For me this is especially true with the double "improved" trilene knot.
I let the tippet material tell me how many turns to take for my clinch knots.
As you're wrapping you'll get to a point where you will begin to feel resistance in the material and that's where you should stop or even back off 1/2 a turn.
For heavy mono this might be 3+1/2 turns and with light X tippet it may be 7 turns. It all depends on the diameter and flexibility of the material.
Knot strength has a lot to do with how well each individual consistently tie their knots. If you find that a certin knot works well for you then you should stick with it regardless of what other people use.
For bonefish flies and other small flies I want a rigid connection with, I start out with a palomar. Any reties are with the trilene. I don't like the "improved" clinch because I think it is too hard to cinch up without burning.
For large diameter bite tippets I use a cinched duncan loop for rigid connections or a modified "Lefty loop" for a no-slip loop. I am tempted to start trying "old school" tarpon flies again, as it seems nobody uses them any more. They were snelled.
I like the Trilene knot, it is exceptionally strong. It is also nice that even if you leave a little extra tag than usual, the tag threads alongside the fly/lure rather than back up the line/hanging outward. The palomar knot is very easy and I use it some times (its especially good when it gets cold and your hands don't want to tie an improved clinch or trilene) but while it rates well with constant pressure some sources rate it very low (50s/60s) on quick stress situations, so I would be nervous using it for tarpon and the like. Also, like Casey said, absolutely lubricate the knot so that it cinches down well and without undue stress on the line. You can also go the extra mile and hit it with zap-a-gap or UV-whatever-its-called, but this could start getting a little tedious...
I've been fishing the Palomar knot for 10 years now, and have never had the line break at the knot. I can't say that for any other knot I use. If it were easier to tie small flies on with a Palomar, I would.
It's the easiest knot I know. Sometime back, someone posted up a knot that was even easier, stupid easy. I think it may have been the Davy knot, if I remember correctly. I checked out a diagram on how to tie it, then went fishing later that weekend, and couldn't for the life of me remember how it was tied.
LOL! I did the same thing right after seeing it. It is mind-numbing easy, so much that I didn't have to do any thinking about it, so didn't have a clue how to tie it later, without dragging up the directions again.
With 60 lb fluoro, it broke well below 60 lbs. With leader that thick it also has a lousy profile, like a sail boat keel and does not cinch up tightly to the hook eye. The standing line comes in either high or low on the hook eye, depending on which way you thread it in and there is another big protuberance on the other side of the hook eye.
When I tried it with a Gami 2/0 (which is pretty thick wire) and 0X tippet, the knot just slipped off repeatedly.
Since guys use it, I'm sure it's fine for small fish on small hooks if you are in a big rush. But the stated strengths are all over the board, depending on who's doing the tying and testing, what line they're doing it with and what it's tied around.
I guess it's just a matter of what you are used to, I am certain I could tie a blood just as fast as you tie a surgeons, not challenging you here, for the fish I catch there really is no need to worry all that much, I am not salmon fishing.