I currently have four djembes, a medium-size lenke from Mali, a very large and squat Jina from Mali (gueni/hare), a lenke from Guinea (Drumskull), and a djalla from Guinea (Mamady).
I also think that the wood has very little to do with sound, as long as it's proper high-density hardwood. I think Nerd's 10% are probably about right, maybe even a little on the high side. It's a different story with less suitable woods, such as teak, mahogany, or tweneboa. These definitely make for poorer-sounding djembes.
If pressed to describe the sound difference, woods at the softer end of the spectrum (djalla, acajou) sound a little warmer and drier than the woods at the hard end (hare, gele, iroko). The harder woods reflect sound more readily, so they tend to sound a little brighter, with slightly more sustain and emphasising the higher harmonics a little more. Lenke and dimba fall somewhere in between.
But I think that these differences get completely swamped by the size and proportion of the drum and the interior carving. For example, changes in the interior surface texture will have a much larger influence on sound than the wood itself. A good illustration of this are Bali imitation djembes that have been turned out on a lathe. I've had the opportunity to compare djembes that had a smooth interior with ones that had a spiral pattern texture added after they were turned. The drums were otherwise the same. There is a noticeable difference in sound between the two. Much less ringing and more body in the tones with the drums that had a textured interior.
The bowl shape and size, as well as the diameter of the port also make a big difference. Of all my drums, the Jina is the loudest, followed by Mamady's, followed by the Drumskull shell, followed by the medium-size Mali shell. It's not a coincidence that this also describes their sizes, from largest to smallest. Larger drums are louder, it's as simple as that.
I don't think that the bearing edge has any influence at all, assuming that it is level and round, without undulations, and has a clean sharp edge where the skin transitions from the bearing edge to the playing surface. I'm saying this because I think that an improperly shaped bearing edge is an easy-to-rectify defect, so mis-shaped bearing edges don't count. (Having said that, a bearing edge that looks like roller coaster will affect sound negatively.)
Proper tuning is important too. Uneven tension, over-tightening, and under-tightening all make for bad sound. I'd agree with Nerd that tuning can account for 30% of the sound. But then, seeing how easy it is to tune evenly, and that it's not that hard to find the tension where a skin "comes alive", I'm not sure I'd be willing to admit that as a factor influencing sound when it comes to comparing different woods and shells.
To me, the most influential factor in sound is the skin itself. I don't know exactly how many dozens of skins I've fitted to my drums over the years, but it's a fair few (except for Mamady's drum, which still has the original skin I got it with in September, yeah!

). I have learned over the years what thickness of skin I prefer on each drum, and I usually select my skins carefully to fit the drum I'm about to rebuild. Yet, despite all my efforts in selecting skins, it can be a complete surprise what a drum will actually sound like once I've fitted a new skin. If I've had a skin on a drum that sounds brilliant, and I carefully select a replacement skin that is as similar as possible, it sometimes happens that I end up with a drum that sounds really poor. Lifeless, anaemic, discordant overtones, and simply unpleasant. The lesson is that skin variation can make the difference between a truly world-class sound and a well below average sound.
So, a good shell is a necessary prerequisite for good sound: a bad shell won't sound good no matter what skin you fit or how you tune it. But a good shell is not a sufficient prerequisite for good sound: the world's best shell can sound poor with the wrong skin.
And finally, technique probably accounts for another 30% or so. The difference between good technique and poor technique in sound is staggering. I've had quite a few students come to me and tell me that they want a "better" drum. When I take their drum and play it, it usually sounds pretty good and they realize that the problem is between chair and drum

Cheers,
Michi.