Ok, I've got to chime in here. Sure, bearing edges, shell construction, hoops, lugs, overall accuracy of build, heads, tuning, etc, etc, all have a huge affect on the overall sound, but all things being equal, wood choice does make a significant, but not deal breaking, difference.
I have a number of stave snares. Pictured below is my Guru Drumworks ebony. I specified ebony because of the sound charactaristics. If I compare my maple stave to my ebony stave, the difference is massive. The maple has a lovely dominant midrange with just enough bottom end to offer weight. The ebony offers less mid range with enhance upper frequencies and crazy bottom end dynamic. Both drums were chosen to perform a specific job, & the wood choice played a big part in that. That said, all other areas of the build were also specified with a defined outcome in mind.