I have found Honduras mahogany to be the least consistent of the "classic" tone woods. The density of the wood, mineral content, grain orientation, etc...can vary a ton. Think about it this way: the "good" vintage 1950s Les Pauls weighed in the 8lb range. 1970s and early 80s Les Pauls (without weight relieving) often weighed 12-13lbs. That's a lot of variation in weight, which can mostly be attributed to the density of the mahogany. I've played mahogany guitars that sound more like humbucker-equipped Telecasters, and others that sounded like they were on the neck pickup the whole time.
As far as the difference that wood makes in the tone, after the string starts vibrating, the vibrations enter the body and neck via the fret and bridge. The wood that the neck and body are made of essentially acts as a filter, deadening some frequencies and accentuating others that are then reflected back into the string.