My experience has been that concert musicians are just as demanding, if not more demanding, about the sound and performance of their drums than a kit player is. Many top-level pros on both sides of that distinction have no idea about how a drum is constructed. I remember seeing a builder friend at a drum show pointing out to a big-name clinician that the drum he was trying out was stave construction, and the big-name clinician looking completely blank because he no idea what the builder was talking about.
Generally, concert snare drums are more expensive than kit snare drums because of the higher cost of cable snares and/or multi-strainers. The tone demands are extremely specific, and the expectation is for highly sensitive response and consistent tone throughout a very wide dynamic range.
We've done concert snares with cable setups into standard strainers as well as with three-cable systems with several levels of precise adjustability. They've been steambent and stave shells, and the woods used have primarily been walnut, rosewood, bubinga and maple. The differences from kit snares are mainly in the bearing edges, snares, heads, strainers and snare beds -- not so much in the shell itself.
It's true I've encountered concert performers who don't know the full world of drums -- not much familiarity with kit drums, for example, or a timpanist who doesn't know snare drums very well -- but that's not unusual. People specializing in a certain type of music often are not well versed in other types of music, especially the gear involved -- this thread is a good example, really. But in a world in which percussionists can spend tens of thousands of dollars on extremely specialized instruments, I wouldn't jump to the conclusion that they don't know or care much about what they're playing on.
It's probably important here to make a distinction between the community orchestra player who isn't making a professional investment into his gear vs. the pro or semi-pro whose livelihood and ability to get hired depend on the sound he produces from the instrument(s). It's like the difference between a fine rock guitar and a fine classical guitar; at a certain level, you can't use one to play the other type of music and get any satisfactory result.