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From Odwiki

Shading Quality determines the final size of a MicroPolygon in the rendering process.

If the shading quality is 1.0, mantra will make each micro-polygon roughly one pixel large. When the shading quality is set to 2, each edge of a MicroPolygon will be roughly half a pixel, resulting in 4 micro-polygons per pixel. Since each micropolygon is shaded once, this will result in more shading and thus, better quality.

RenderMan uses the shading quality to determine how many micro-polygons will be generated for a pixel. So, setting the shading quality to 2 will result in roughly 2 micro-polygons per pixel. This is different than mantra.

To get equivalent shading quality between RenderMan and mantra:

  RenderMan shading quality = sqrt(Mantra shading quality)
  Mantra shading quality = pow(RenderMan shading quality, 2)