I have the D7100 for wildlife and the only criticism is the slow buffering, however I have learned to live with that quite successfully.
I have used the D800 for shooting wildlife very successfully, not least because of increased buffering speed, but the reasons I don't use it more often is twofold. Firstly, reach. I find the x1.5 crop, apart from the extra reach, enables the centre of long FX lenses to give excellent sharpness. Secondly, weight. The combination of the D800 with any long lens handheld takes my strength after prolonged shooting sessions and generally carrying about. That said I am not as young as I was and this may not be a problem for others.
Regarding the D600 v D800, I have used a friends D600 a few times and it's a very formidable camera, certainly great value for money. However, I prefer the D800 and this is my landscape, architectural and portrait camera. I mostly downsize my images on import to 16Mp which enhances sharpness, which leaves plenty of pixels to play with. Also, I like having an AF-ON button for when I do use it for wildlife.