In regards to guitars, Koa is a bit brighter than Mahogany and works really well for fingerstyle. To me, it's just too bright for anything other than fingerstyle, but again, that's just me. Guitars built with all Mahogany are mellow and smooth, brighter than rosewood, but not too bright. Put a Spruce top on a Mahogany guitar and it becomes brighter.
Regarding ukuleles, to me Koa has the "Island" sound, and Mahogany has more of a vintage sound. Today, Vintage Martin ukes are the most sought after ukes there are in the terms of collecting. They have what most call the "Martin" sound. That sound is a sound tha many builders have tried to duplicate for many years. Kiwaya is one modern builder who models many of their ukuleles after the Martins of the past. They have succeded pretty well with their Sopranos, but their Conert and Tenor sizes, although very good in their own right, just don't sound like their Martin counterparts.
In terms of tone, I have heard many who prefer the "Martin" sound not because it's a Martin, but because they feel they can control the tone better than they can with a Koa uke. Keep in mind that when I refer to the "Martin" sound, I am refering to ukes made of Mahogany. This is of course personal preference. But basically, what they are saying is the more mellow tone of Mahogany can be controlled easier with different strumming and picking techniques. Koa isn't as easy to control for some players. I know a lot of uke players from the Martin Guitar Forum, and this is something that most fo them agree on.
As far as pricning, I am willing to bet if any of the big Hawaiin builders started using Mahogany, the pricing would be right up there. For starters, Genuine Honduran Mahogany is getting to be quite scarce, and it's status with C.I.T.E.S. is gradually changing. Simply put, we wont have Mahogany around for much longer, much like the situation with Brazilian Rosewood. As it is, guitar builders like Martin can't even get good quality Mahogany neck blocks in the quanities they need to keep up with thier production. Many of their guitars now sport Spanish Cedar necks instead of Mahogany necks. I'm not sure how Koa is doing with C.I.T.E.S., but with all the building going on, it probably isn't to far off from Mahogany.
Anyone wondering what C.I.T.E.S. is, it is a UN group that oversees the agreement to protect endangered species, including animals, as well as flora and fauna, which would include endangered trees.
A lot of the "Mahogany" ukes on the market today are not even made with Mahogany. They are actually make with Sapele, which often goes by the name "African Mahogany". Sapele is not even in the same family as Mahogany, but has a tone almost identical to Mahogany Also, a lot of Mahogany or Sapele ukes are being built in China and other countries where a uke can be built and sold for pennies on the dollar. So, maybe this gives the perspective of being cheaper versus Koa. This is a false perspective and not a fair comparison. As I said above, if any of the if Hawaiin builders started using Mahogany, they woudn't be cheap. If anything, they would probably have a better value down the road in terms of collecting.
As far as player ukes, I would say that no wood is better in regards to tone. It is really up to what they player prefers. I have one really nice Koa uke with another on the way. I also have a cheaper Mahogany uke coming too. I have no idea what the Mahogany uke will sound like, I'm just hoping it will satisfy my desire for a Mahogany uke until I can save up for either a Custom or a Vintage Martin. I prefer tenor sized ukes, so for me, the selection is even smaller when it comes to Mahogany.
If you love Mahogany, keep loving it. If you want a high end Mahogany uke, you will probably need to go custom, or seek out a nice Vintage Martin. As far as Walnut, it is described as sounding very much like Koa, and Maple would be pretty close to, maybe even a bit brighter.
Sorry for such a long post, I just wanted to dispell the notion that Mahogany was cheaper, and I wanted to share from other perspectives.