Update: Nikon issued a firmware update, now the D600's HDMI output works as it should, with 100% frame coverage.
Comparison of the uncompressed Live View HDMI output of the Nikon D600 and the D800.
At this point, the D600's video mode is limited due to a black frame around the HDMI video stream, similar to the D800's 95% HDMI output display size in the advanced system menu. Furthermore, it is not possible to change the aperture when Live View is activated and there is no live histogram.
The D800 doesn't have these shortcomings.
At the end of the video, you see a comparison between Ninja HDMI recordings from the same tripod with the same focal length and same settings to compare the black border and the field of view.
I wouldn't suggest to use this to rate the cameras general video quality due to the strong compression, which is needed to upload to vimeo.
If you have any questions or suggestions feel free to ask me in the comments.