The volumetric one looks more stylish and professional to me than does the flat one. I think the flat version has too much of an angular zig zaggy look. Particularly with the smaller lists where it is, for me, harder to make the necessary visual separation between the adjacent lists because their frames "jigsaw" together like that. I like the fact that the volumetric one has much better framing of the option lists. Generally square boxes, or rounded square boxes, with fancyish borders are better...more in line with UI standards found in all software interfaces, and therefore more familiar.
I prefer the volumetric one because it is more beautiful and attractive. I also think it expresses the medieval theme more effectively...like signage commonly used to represent that era.
I vote for volumetric over flat.