Maybe the OP want to just focus on the wood in general situation, and I see no confuse on the thread title. Sometimes focus on single matter can get clearer idea. Then put all the ideas together for the whole picture.
Next questions can be "Thickness of sound board", "Bracing pattern", etc...
No offense here. I am not suggesting the model answers that seems everyone know that "wood is not the only matter" "the way of how it is built is more important" etc...
From what I have read and I believe, Koa has wider dynamic range than Mahogany, more high end. It is quite true from the real world I've tried. But I am lack of experience to compare. This is only base on my very little experience and un-trained ear, of playing and listening one by a time in a quiet room every night.
Mahogany sounds louder in mid-range, this louder sound may give a "sound brighter" confusion. At where I live everyone in the learning lesson play Mahogany, in ukulele shop its the most familiar sound.
Koa sounds more focus/solid, more high-range sound. Some people believe tonewoods will open up in time, when this happens to Koa, it gives more low-range sound. I have played Koa not long enough to experience the open up process. But I played on a acacia black wood long enough to notice the "open up" thing. This should be similar to but not as good as Koa.
Spruce, absolutely loud, bright, more high-range sound. Once I touched the spruce one, I hear guitar.
A while ago I have read about tonewood in somewhere, and this picture is the idea from my memory.
These are just my inexperienced opinion. I wish someone wiser in this regard could correct me and teach us more.