Right now I'm very much still on honeymoon with the D600 so I am taking it pretty much everywhere. But once I settle back in to my typical routines I'll likely reserve shooting with the D600 for most paid gigs, special events and any photography specific trips. Seems the 24-120 f4 VR is finding an almost permanent home on the D600 but I have a nice line up of FX primes too.
My DX body is now a D5100. It's a fraction of the weight and size of the D600 so I'll pack that when I need to travel light, for me that's on multi-day backcountry treks, family occasions and any time I want to be less obtrusive. I have several DX lenses like the 35mm f1.8 DX that make a great, small-kit combo with the D5100.
One scenario I will need to adapt to is wildlife shooting. My longest lens is the 80-400 VR which doesn't autofocus on my D5100 so while I typically would of taken my ex-300s on wildlife shoots, I suspect for now it'll be the D600.
Depending on price, size and weight I could foresee swapping the D5100 for a D5200, D7200 or other future DX body to regain the DX reach in a better body. I'm not so thrilled with the 5100's AF.