HDRI images contain the full range of colors. But unfortunately there are no monitors which can display this complete range. You need an image editor which can read the complete range and allows you to define the selection you think your image needs. So effectively this is post processing.

In Poser Gamma Correction corrects the color to its true values. These values are used to make the material adjustments. So this takes care of the contrasting shades you mention. Saving these in HDRI gives you the full range of shades and colors which are present in the image.

Now with the full range you can use the image editor to pick the shades and colors which fit your interpretation of the image.

It is a really complicated thing to explain - search the web for colorspaces, color palettes and the 16, 32 and 64 bit color image file specifications and you will see the wide variety of choices you can make (or better - the limitations you run into)

I use a professional monitor which has a much larger color spectrum as a "normal" monitor and the difference can be dramatic. The same HDRI image just looks dull on consumer level monitor because less colors are displayed.

So concluding - Is it better to save in HDRI format? Yes, but you need to post process it to make it available for other users on a computer