The photos I get now from my D300 still look as good as the ones I took when the camera was new. But there's another aspect of the D300 vs. D600 that hasn't come up in this thread.
It's not just "upgrade your camera and get better photos." Because the D600 is an FX camera, it's also upgrade your camera and lenses, and carry around a bigger heavier load to get those photos. You just can't swap out a D600 for a D300.
I'm using a Sigma 10-20 as a wide angle, for example. With a D600 I'd need a 14-24 or 16-35 to go as wide. Not only are they expensive, most of the time I don't want to carry lenses that big and heavy, so for me, the DX lens is better, even though image quality may not be quite as good. (But, I've made some very good-looking 20"x30" prints with that lens!)
Similarly, my most-used telephoto is the DX 55-300, which is small and light and easy to carry. (It also has excellent image quality.) I also own an 80-200 f2.8, and an 80-400VR. I could use them on a D600, but they stay home most of the time because they are big and heavy.
Do you really want to carry a bigger and heavier FX kit to "upgrade" to a D600? The point is, you would not just be swapping cameras in the move from a D300 to a D600, so any evaluation has to take into account more than just the image quality of the two cameras.