Digging through the EagerEyes archive, Robert Kosara demonstrates the little known square pie chart. I am not joking. Think pizza sliced square versus "normal" cutting. Kosara convincingly shows how a square pie chart makes it much easier to read the raw magnitude of a statistic.
Another thing that's apparent from the discussion, under the assumption that the graphics are on the same scale, these charts support comparison quite well. Magnitude directly maps to area. Square pie charts also strike me as a fairly flexible basis for an interactive visualization, being pretty straightforward to generate, scalable, and quite button like.