In general terms, Koa does have more clarity and articulation than mahogany. But all wood varies, and in the end it is just the luck of the draw. Plus, it depends on what species of mahogany you are talking about.
Personally, I like Koa acoustics better than Koa electrics.
Listen to PHISH records from around 1997 onward and you can hear Trey Anastasio playing a koa hollowbody.
I think his tone is killer with koa + an ebony board.
Before 1997 or so he used a guitar made from other woods.
You can hear the tone change from the earlier records to the later records when the koa guitar became the main axe.
Instead of saying koa is bright (which I disagree with anyway), I'd say that it has a little less bottom to it than mahogany. As a result, while it has less bottom, it has tighter low-mids. Combine that with a pau ferro neck (dark sounding) and you have an amazingly thick but articulate guitar for high gain sounds. AWESOME CHUNK!
Personally I think of KOA as brighter sounding then Mahogany, in Acoustics I would compare it a Flamed Maple acoustic.
But dominant tone from a guitar comes from Body, top and neck so there are ways you can "tweak" things. Choose a top that doesn't sound so "bright" (Cedar for acoustics or Adirondack, Rosewood type top for Electric) and a neck that is not so "bright" (Mahogany, Rosewood with Rosewood board)
My Koa/Cedar acoustic is the best sounding acoustic guitar I've owned.
I have two acoustic OOO size guitars, both made by the same builder. Both have Cedar tops and the same neck/fingerboard. One has a mahogany body, the other one koa; otherwise they are identical. Both sound quite similar, but there is a sweetness and balance in the koa guitar that gives it the edge to my ears. It's not the same as a maple body either-but it does seem to have slightly less bottom than the mahogany guitar.
As Scott pointed out though, every piece of wood is different-regardless of wood type. I also don't know that acoustic observations will transfer to electric solid body in the same way. (I do intend to find out though-my next project guitar is a 3-P90 hollow koa strat....)
Don't be afraid to try different woods because there are many great wood combos out there that yield excellent tones.
One thing to consider is learning to dial in your amp for the particular guitar you are playing.