You're right, the flame graphs (which is really an adjacency diagram with an inverted icicle layout) doesn't exaggerate subdirectories like a sunburst layout does. I wrote about problems with the sunburst layout before in ACMQ[1]:
> The sunburst layout is equivalent to the icicle layout as used by flame graphs, but it uses polar coordinates.7 While this can generate interesting shapes, there are some difficulties: function names are harder to draw and read from sunburst slices than they are in the rectangular flame-graph boxes. Also, comparing two functions becomes a matter of comparing two angles rather than two line lengths, which has been evaluated as a more difficult perceptual task.10
(I should have mentioned that they visually exaggerate deeper slices, too). I think they are pretty, but, more difficult to read.
The other app has a pie chart and trees. Both can't visually show everything at once, all subdirectories.