OK, I did a comparison on my scene with various combinations of Hemi/HDRI, Sun, and Sun/Sky lamps.
My original scene has the HDRI along with a Sun/Sky lamp, and hence tends to be bluish. The lesson here seems to be that the best image is obtained with the HDRI and a Sun lamp, but make sure to turn off the sky portion of the Sun lamp.
Settings - Light groups set for Sun/Sky = 0.25 and HDRI = 10,000. Did not have dispersion turned on so the scene would converge quickly. (30 minutes each)
As a curiosity, having only an HDRI and a Sky washes out to pretty much nothing.
Note how the white table surface shifts color/white balance depending on illumination source.
Also note that the Sun only image shows 'black' diamonds. The brightness of the gem is dependent on reflecting the environment around it. Even the Sun/Sky combination looks dull. "Watery" comes to mind.
Again, to me at least, the clear winner is the top right image.
Brian