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Living in South Dakota, I shoot my share of wildlife. I am also a very hardcore night photographer. (In winter I mostly shoot at night.) I tried the D600 briefly, didn't like it. I see only see disadvantages for it with wildlife. First, you lose the reach. Second, the AF is noticeably slower than the D7100. Third, the D7100 can focus in lower light. Fourth, the D7100 has better sealing, more solid feel. Fifth, the pixel density is much higher for the D7100--a good thing. For wildlife, the D7100 is a no-brainer. I wouldn't even consider the D600 for that.
NIght shooting. The D7100 shines! You only get about one more stop of ISO with the D600, for which you pay a bunch more money. Add to that the D600 does not focus in low light as well as the D7100. Here's another angle on night shooting. People make a big deal out of ISO, and sometimes it does help depending on your subject (i.e. moving.) However, the most famous night shooter of ALL TIME was a guy named Brassai. He used a Voightlander Bergheil shooting glass plates that had an ISO somewhere around 10! This was in 1930, and his shots are stunning! I routinely shoot my 1940s vintage Leicas, Rolleiflex, and even old Kodak Brownies with ISO 400 film and get great results. Last weekend I was at the big rally in Sturgis, SD with the Leicas and the D7100 and got some great night shots with both. Again, the superior autofocus of the D7100 seemed more critical on fast grab shots than the ~1 stop ISO advantage of the slower D600.
Bottom line for me is that no one I show photos to will ever see the difference between shots made with either the D7100 or D600, and that includes my paying customers.
Kent in SD