John, appreciation depends on the audience. When woodworkers look at furniture we look at joinery and difficult to exeute design elements. A casual observer goes for the visual impact first. I have made some small boxes that I really like because they contain handcut finger joints in lacewood. But I get most comments on a hall cabinet I made which has an Olive Ash veneer on the top. The top was the easiest part to make, the burl was already there all I had to do is glue it in place.
The way I look at it we have to balance both aspects of a project, unless you are making it for yourself. I think your chest is great, but I bet if you had chosen some kind of figured wood for the drawer fronts you would have gotten a lot of oohs! and aahs!
The means by which an end is reached must exemplify the value of the end itself.