I have to agree with Beej, post#155. Everything matters. And maybe someday, someone will find the time and money to do exhaustive tests, on which things have the most, or least influence on sound/tone, that most people will be able to acept the results from.
While I have used maple, rosewood, ash, alder, poplar, wenge, mahogany and a few other generaly accepted instrument woods, most of my guitars and basses have been made from combinations of Australian native woods.
As a result I've formed a general view that density, hardness and weight, (because weight is usually in ratio to density/hardness) may be more crucial, or just as crucial, to any changes in sound/tone, than actual species.
Using Australian woods of approximately the same density, hardness, weight of the commonly accepted 'tone woods' in use, and adding the same range of hardware, construction methods , pickups, controls etc. can produce incredibly similar tonal results. I'd never say identical, because I doubt any two instruments constructed from wood, can ever be identical, if they were measured under strict scientific test conditions. But we're largely talking human ear level of judgement.
I also know that two pieces of wood of the same species can vary a little, or a lot, depending on where they were grown, etc. that doesn't change them completely, but it does shift the ballance of frequencies enhanced or diminished. As a result, I'm a bit wary of blanket statements about this or that wood, giving this or that result, we're not talking about a repeatable man made product here, like a particular plastic or steel.
Just as an example, since 1977, I've used Tasmanian Blackwood quite a lot. It's a close relation to Koa, looks quite similar and weighs in the range of 5% more than mahogany and is about the same percentage harder/denser, (there's that relationship between weight/hardness/density). I think it adds similar sonic qualities as Walnut, which just happens to be average weighted at 40lbs per cubic foot and a Janka rating of 5,030, while Blackwood is average rated at the same weight but with slightly higher Janka rating of 5,180.
Having said that, about averages, I have used slower grown Blackwood from high altitude forests that has weight as much as 30% more than the average and I'd expect that sort of variation isn't uncommon when it comes to wood.
I'm in the wood makes a difference camp, but I'm pretty sure that it isn't top of the list, though in some small sample situations, the difference it might make could be outside the norms. I'm sure in some cases, the examples like, 'I have two P basses and the only difference is the ash and alder bodies and they sound completely different', is true. But one swallow (or even a few of them) doesn't make a spring', as the old saying goes.
One thing that has to be said about testing, is that every aspect must be exactly repeatable and the process must be as near as possible free from possible irregularities. A repeatable mechanical method for striking the strings is a given, even the best human can't perfectly repeat the striking of a note, at a level to provide truly accurate scientific data. A control and pickup module would be needed that can be positioned exactly the same for each sample and any screws, nuts, etcetera, would need to be tightened to exactly the same degrees of force. All samples would also need to be recorded exactly the same, meter reading might show clear or subtle variations, but at the end of the day, will the human ear hear them? So blind test recording samples.
Still, at the end of the day, with thorough monitored testing, would humans, listening to the results, be capable of forming judgements on the results free from bias/influence? If told we were about to hear the results of some tests for tonal differences between different woods, would we hear differences, because we expected to, or not her differences, because we expected not to? ( Sorry, couldn't resist...
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Whatever the properties of the wood for it's intended application, as a builder you just factor those in and make other construction choices to achieve the same goal. 
