I'm extremely pleased with my recent switch from the D300 to the D600, but I had a few more full-frame lenses than you will be starting with. I use an 85mm f/1.4, the 105mm VR and a 70-200mm. I also use the 50mm f/1.8 that you have, and it works well on the D600. In fact, it stays on my D600 most of the time right now until I purchase a full-frame zoom. I also added the 20mm f/2.8 recently, and it is great for landscape.
The difference in overall image quality for me has been large and made the switch worth while in every way. I'm now taking indoor shots with no flash that I would have passed on when I was shooting the D300.