From what I've experienced going from the wood bodied to the stone platinums is that the woodies have the classic Koetsu sound. Higher in output voltage these are very rich but have their ficus on the midrange. The higher density stone bodies, higher still than even the Urushi laquered woods, along with the platinum motors are more extended in the extremes and tighter as well. If the woodies are colored, the stones are technicolored bot beautifully so.
What I haven't heard at length are the diamond cantilevered Koetsus. My observation is that among the stone bodies the Jade which has the highest MOHs rating among the line that I know of, is the quickest and punchiest. The lightest Blue Lace (Agate) the most delicate and etherial with the highs followed closely (very) by the Tiger Eye andthe Coralstone the most flexible having many attributes of the others. Despite the greater extension of the stone bodies, there are many carts out there that do the highs faster and cleaner and the bass tighter and more tuneful. As far as the mids are concerned there are few that IMO really resemble the Stones or any Koetsu that matter. Among these that I have encountered are the Miyabi and the Shelter Harmony. Surprising to me is the new generation of Lyras which have injected more body into the Lyra house sound. Then again given Stig's long time friendship and relationship with Sugano-san, I shouldn't be surprised.
Koetsu's play all kinds of music well. I think every serious alanog guy should own at least one, if only for the history. Personally I love the vintage sound one can get from Koetsus. When I am in the mood to get a retro vibe with jazz, funk, classic rock and standards I do like to use my Jade even if there are other carts I have that do things just as well but differently.