Well, I also have no idea what their intended purpose is. I only got my Inova X5 in green because it looked cool.
From my use, though, there are a few things that I can say about it. Being that our eyes are pretty sensitive to variations in green wavelengths, shining a green light at something still gives you pretty good differentiation between color regions in the visual field.
Now, while I wouldn't say that you have good color rendition with monochromatic green light, the contrast between colors remains fairly true to what you see under normal white light. That is, under the green LED, you don't see a deep red as red and a happy yellow as yellow, but the red still appears relatively darker than the yellow. It's the same sort of thing as converting a photo to black and white - you don't see colors anymore, but reds and yellows and blues, etc. are still different shades from each other.
Another thing I've thought about, though haven't had the means to test, is the use of green light for aiding night vision. Red is considered good for night vision because only the cones in your eyes see it, and the rods can remain adjusted to the dark, as they aren't sensitive to red. Green, however, is pretty close to the color that all optical receptors are sensitive to (I think it's yellow-green, about like many safety vests, fire trucks, etc., to be precise). So, being that our eyes are more sensitive to green than to either blue or red, I would hypothesize that one could use a dimmer light to achieve the same ability to see. And if you're using a dimmer light, would you not be preserving your night vision to a greater extent?
Also, since both cones AND rods are sensitive to green light, a green LED for night vision would provide you with much better peripheral vision than a red LED, as your peripheral vision uses mostly rods. By the same token, of course (as alluded to above), since red isn't perceived as well in peripheral vision, it would make a better choice in many tactical situations.
Anyway, I personally like and use green LED's for preserving contrast between colors, as opposed to red (where, for example, reds and yellows become indistinguishable) or blue (where reds turn way darker than normal). Of course, I'd be curious to hear more about the intended purpose(s) of green light...