What does the 1Dx offer over the 5D3? Well, I suppose it's about what you are shooting. I've shot with both a fair amount during sports for sure. The 1Dx AF is more accurate and seems to be quicker. If a player is running, during the burst of exposures, the player stays in focus, even while moving, that is, the AF can still track even during a burst of 8 frames. The 5D3 did not have this luxury, and the frame rate wasn't nearly as much. Swimming comes to mind, when during the butterfly, you want the swimmer at the top of the motion. With the 1Dx's burst rate, this is easier to capture at the perfect time, vs. the 5D3. Not to say it cannot be done, however.
Shutter durability is definitely a huge factor. There are other things though. In the 1Dx you can set min/max apertures/shutters/ISO's. This allows you to use EC with auto ISO, and still select your shutter speed and aperture (or any combination). Certainly not a feature in other series models. I use a f/2.8 lens and set min ap to f/2.8 and max to f/1.0 in Tv mode. This locks the camera at f/2.8. I then choose a shutter speed at say 1/500, and using CWA metering can use auto ISO and still set an EC value of +2/3. So I'm effectively doing +2/3 EC in manual mode with auto ISO and every single shot is +2/3. How cool!! This can be very, very useful and can contribute to my lazy lifestyle! Not the best in every situation, but certainly where light is low and even.
RAW files are also easier to clean up and edit. Not a huge difference, but a huge difference at ISO 6400 for sure. Shoot mRAW with each once at 6400 and see how much better the processing internally is for the 1Dx than the 5D3. It's amazing.
It is worth the extra price over the 5D3, for me at least.