Well, I own both cameras (as do several other members of this forum) and if you want my main differences, I'll share them.
The first is spot-metering. Sometimes I use spot-metering, let the camera read back the settings, then I make a decision what to set everything to in Manual mode. The nice thing about the 1DX is that spot-metering is linked to any active AF point, whereas the 5D Mark III only does so at center. This is useful in certain situations.
The next things are the dual-cross type AF points on the 1DX down the center, and face-recognition AF is 61-point or zone AF is selected. Again, this could be very useful in certain situations.
The biggest thing for me is EC in "faux M" mode. With the 1DX, in Custom Functions, you can set shutter speed ranges and aperture ranges (CFn.2) and also use ISO Safety shift (CFn.1). So what I can do is set TV mode to 1/500 let's say. I then can set my minimum aperture to f/2.8, and maximum aperture to f/2, if I'm using a 135 f/2L. I then turn ISO safety shift to ON. I can now set EC to whatever I like, such as +2/3 or +1 or whatever you'd like. I've pretty much just transformed TV mode to M mode with EC. What the camera will do here, is if there is not much light, will widen the aperture to f/2 FIRST. If there still isn't enough light, it will then raise the ISO value to whatever need be. This is just an example. You can do it in AV mode with min and max shutter speeds as well.
12 fps is really cool too!
The 5D Mark III has advantages too. Its silent shutter mode really is silent, and I utilized this feature at the tennis matches and golf matches I was shooting. Really usefull feature.
The 5D Mark III's biggest advantage is resolution. 22MP becomes significant with heavy cropping. I have taken samples with a 70-200 f/2.8L II IS lens and cropped the same ratio, and there is more detail loss in the 1DX files. What is odd though, is that the 1DX files remained just as sharp looking as the 5D3 files, and more highlight and shadow detail could be retained with the 1DX files. So there is actually going to be an IQ difference for pixel peepers, both good and bad for each camera.
In auto ISO in manual mode, the 1DX will expose "darker" than the 5D Mark III. This is well known. There is good and bad to that obviously. To avoid that, if you have a 1DX, use EC.
Both cameras are truly excellent. Consider the main differences and decide what you really need. When my nephew was born, I took all of the photos of him for the first 3 months with a 5D Mark III and various lenses and I am so exceptionally happy with the camera! I have also shot a ton of sports with the 1DX, and again, much more satisfied with that camera than when I had the 1D Mark IV.
Good luck in your decision!