D5300. Safari equals stationary and moving animals. Dslrs are just better at focus tracking still
I may contradict my statement above, but I can agree to this. I've had the Nikon D5100 and I currently have the Olympus OM-D E-M5 II. The focus tracking with the Olympus takes some getting used to. ...by this I mean using Manual focus for fast moving birds. On stationary or slower moving objects, the auto-focus is very fast and accurate!
I tried using my OM-D E-M5 Mark II along with the M.Zuiko 75-300mm lens for shooting Osprey's and other various flying birds at the beach, using Continuous Auto Focus. I found the lens hunting for the focus, which was very frustrating, as I got very few "keepers." I'm not sure if it was the camera or the lens's focusing ability. I ended up switching to manual focus, and found the "Focus Peaking" offered in the Olympus a very useful tool, increasing my success rate exponentially.
Now, to be fair, I had not yet used this camera for this purpose, as I've only had it for a month or so. (I also did not purchased this camera for this purpose. I bought the Olympus package for it's small travel size). The settings in itself took some getting used to. By the week's end, I was starting to get the hang of taking some really sharp photos. Practice makes perfect, and I know I could get sharper photos now that I am more familiar with the camera and it's proper settings.
With that said, Given the choice for your Safari purpose ONLY and no other variables, I would go with a Nikon DX body with the 70-300 VR II. You will probably not be disappointed.