Here are some tests I did of a friend of mine. All have exact same settings. The D800 and D800E are much more filmic that the D600 and appear to have better latitude. The D600 has more moire and aliasing. The D800's mostly show aliasing in the t-shirt. It's really hard to see with the vimeo compression, but the D600 has a lot of aliasing in his hair and beard, and has some slight color noise on the skin. It was raining here in Miami when I did the tests, so that's what you see out the window behind him.
Very strange, but the D600's sensor seems to cover a wider area.
All are out of the camera without any correction. I used the Flaat_11p picture style in all cameras. The Flaat picture style used was really created for the D800.
The D600 is a pretty good camera for the money, but the lack of f-stop changes during live view, and the fact that you get a black box around when recording via HDMI, really makes the D800 worth the extra $900 bucks. The D800 is a very robust and solid camera and is made in Japan, the D600 is made in Thailand.
Here are settings:
1/50 sec @ f5.6 ISO 160
Daylight WB setting
Flaat_11p picture style
Nikon AF-S NIKKOR 200mm f/2.0 G ED VR Lens