Interesting that the D600 ISO score is better than the D610.
I didn't check out the camera comparisons until just now, but I will say that in a comparison of the low light theater shots (jpegs as I don't have RAW from the D600), I did notice the jpegs at ISO 1250 straight out of camera had slightly less noise on the D600 images.
Another thing I noticed is the D600 focused faster and locked focus better in low light than the D610. At first I didn't know why the D610 would refocus when I held down the shutter button then recomposed, but then I noticed that the little focus dot inside the viewfinder wasn't lit up because the camera hadn't achieved focus (AF-S single point for both cameras). This happened numerous times during the theater performances and even here in the house without any additional lighting used.
I think someone once mentioned a possible compatibility problem with non-Nikon lenses, and since my 24-70mm and 70-200mm f/2.8 lenses are both made by Sigma, I do question whether that is a factor. So...I am opting to rent a Nikon 70-200mm f/2.8 for the theater performance this week to see if there is any improvement (I don't get paid for the theater photos, but I really want to sort out whether it is a compatibility issue or a low light issue). Of course, the stage lighting is minimal...only a couple of spot lights. I've been using ISO 1250 trying to keep my shutter speed at 1/30 or faster with an aperture of 5.6 whenever possible; however, periodically I do have to use a wider aperture when my shutter speed falls below 1/30. Yes, I know I can switch to a higher ISO, but it's because of the noise that I choose not to. The curtains are black, and since the lights tend to be limited to two spot lights, I meter for their faces. That means the surrounding areas are darker, and when raising the shadows, the noise increases. I used RAW for their March performance and had to tweak the overall exposure to bring up the shadows, but it also increased the noise. For a few photos, I used my D90 with my 24-70mm lens as I can't quite fit the entire stage in the viewfinder with the 70-200mm lens (beats having to switch lenses so frequently). I can definitely see an improvement with the low light capabilities using the D610 over the D90 though.