I can only state what my thinking is... I have owned the D200 since the day it was released in the US. When the D300 came out (and later the D300s) I looked at the specs and the sample images available and decided that, although there were definite improvements, the improvements in image quality were not enough to make it worthwhile for me to upgrade. Although the autofocus system seemed to be a significant improvement over the D200, my camera was working fine for the images I was capturing - again, no real incentive to upgrade. There were other improvements but none of them, even in combination, provided a compelling reason to spend the cash for a newer camera. As always, your mileage may vary. As a side note: My D200 takes pictures today just as well as it did when it was new and since I have learned more about how to use Photoshop the final results are even better than they used to be.
I think you need to evaluate your experience with the D200. Where is it letting you down? In what way is it holding you back? How is the D200 preventing you from capturing the images you want? Once you have done this evaluation you will know what you need in a new camera body to achieve the results you are after. When you know what you need in a new camera you can then evaluate the D300s or D600 (or any other camera) to determine whether it has the features and/or performance that you need.