There is a difference between DX and FX models when it comes to wide angle. They don't have the same angle of view, counting in the 1.5 crop factor. They have the same field of view. At most focal length you won't notice the difference between them, but a super-wide angles it's there.
Say you have a 12mm DX lens and an 18mm FX lens. Yes, you'll get the same width of frame, but the 12mm lens will give a greater depth of field, generally produce more edge distortion as well make close objects, like the foreground feature in a classic landscape, appear closer and more separated from the distant features in the scene.
If you don't shoot landscapes or interiors, this probably won't be a big deal. I do, and it is for me. I went with the D600 and don't look back. OTH, if you shoot sports or wildlife, that 1.5 crop factor comes in mighty handy.
The other consideration is shooting available low light. The D7100 would have been amazing just 4 years ago, But the D600 will give you about 2 stops less noise. I also shoot theater, where flash is not allowed.
BTW, I needed one sensor cleaning, as I got a very early mode D600l. Some 7500 shots later, my photos are free of sensor crud.