Okay, some of this might have been covered already but here it goes. The three most common woods being used for mid to upper level drums set are Birch, Maple and Mahagony.
Birch has a fundamentaly brighter tone and higher pitch and is arguably a bit louder than maple or birch and offers a bit more projection.
Maple, while still loud is going to have slightly less projection than the birch but a fuller attack and slightly lower fundamental tone.
Mahagony is not going to be as loud as maple or birch but is going to have a much fuller tone because the mahagony has a naturaly lower tone and gives that big fat bottom end that many drummers look for.
This is the thought process on an even playing field and having three drums that are constructed identicaly to each other but there are a ton of other variables. As was mentioned earlier, bearing edges and reinforcement ring construction have a major impact on the drums with some companies offering 45 degree or dual 45 degree bearing edges and many vintage drums having 30 degree or rounded bearing edges that would creat lesss attack and more warmth to your drum tone. Other things to take into consideration are the number of plies and thickness of the plys because a thicker shell is going to creat a higher pitch with more attack and less resonance and a thinner shell will resonate more and creat a lower tone on the drum. Two other variables are the age of the wood and head selection. A three ply maple Ludwig kit made today is not going to sound exactly the same as a three ply Ludwig kit made in the 40's or 50's brcause the wood in the older kits has had decades to dry out and give the drum a warmer character. Lastly, you can alter the sound of any kit greatly by simply changing up the heads that you currently have on your kit but that discussion alone could take up a lot of space on the board.
In the end, one wood isn't any better than any other, it is all a matter of personal prefferance and what I like or someone else likes may not be what you like.
Many of the "Maple" kits that had outer wraps on them also had an outer ply of mahagony under the wrap because the glue that was used to apply the wraps adheared to the mahagony better than it did to the maple.
Hope this wasn't too much information.