I have tested my 600 f/4 with the full range of teleconverters on the D300, D7000 and D800E.
The D800E and no teleconverter produces the best results. I'm not sure I would readily recommend any of the alternatives using a teleconverter. Likewise best results are from closer range - inside 100 yards. When you are photographing distant subjects, any vibration starts to be more of a problem so shutter speeds need to be kept very high.
The various combinations of D300 and D700 suffer in comparison. And with controlled testing in the field, I could not match the sharpness of the D800E and 600 f/4 using any of the teleconverters.
Now this does not mean the images were not usable. My context is the exceptional sharpness I have with the D800E, great lighting, and a close subject with the 600 f/4. I can still sell and make relatively large prints from images that are not at maximum sharpness. But you do lose some ability to edit, extract detail, and optimize a slightly soft image.
In general, I would rate sharpness of the 1.7 and 2.0 teleconverters to be the same. The issue is the loss of light - and therefore shutter speed.
Now perhaps you can get sharp images with the long telephotos and teleconverters, but you'll need to have impeccable technique in all respects. You'll also need to make sure gear is appropriately calibrated. And if you are talking about cropped images of distant subjects, it's all about what compromises you find acceptable.
The 600 f/4 is a big heavy lens, but it's the sharpest lens I own. The reason for the 500 f/4 is a lighter and smaller lens - and you are willing to sacrifice a little reach. Teleconverters will impact both lenses in the same manner. But I think you should use a teleconverter as an exception and make your decision based on the bare lens.