Both the D600 and the Df use Nikon's Multi-CAM 4800 AF module so focusing performance should be similar (differences in processors can effect the speed even between cameras with the same AF module).

Those lenses are nice and fast - which should help but the bottom line is the AF system needs contrast to acquire focus. You can help by keeping to using only the 9 cross type sensors in low light and looking for contrast edges in the image and using them to focus on. Things such as door or window edges, the edge between bags and other things people might be carrying, belts, shirt neck line etc.

According to this: https://imaging.nikon.com/lineup/dslr/d600/features02.htm there are only 9 cross type sensors not 15. I must have mixed the numbers up in my head while I was reading about various AF modules (answer corrected). That article has a diagram showing which sensors are cross type and which are single.

The difference between cross type and single type sensors is in about how they detect the contrast that they focus on. The basic building block of these AF modules is a sensor that can detect contract along a certain direction. Consider a window frame if you line up the AF sensor so that its ability to detect contrast crosses the frame - in other words the sensor can see part of the wall and part of the frame it will be able to detect that change in contrast and focus on that frame / wall edge. If you tilt your camera so that that AF sensor now runs parallel with that frame there is no contrast to detect: the AF sensor sees entirely the smooth wall or entirely the smooth frame and therefore sees nothing to focus on. Obviously the sensors are not laid out straight up and down or we would hit this frequently with geometric things. With non geometric thins like people you can hit this problem from time to time. In the AF module this problem is tackled by having some sensor points actually have two AF sensors oriented as a cross. Those sensors cannot be fooled the same way because there is no orientation that they cannot see contrast. These sensors also tend to perform better in low light situations. I don't know if it is because they typically are better sensors or the fact that there are two of them working together helps with low light situations.

As for better the D5, D850 and D500 share the Multi-CAM 20K which is supposed to be a significant step up in AF performance. While the D750 and D7500 share the Nikon Advanced Multi-CAM 3500 II which despite less sensors is also supposed to be better than the previous generation.