I have both bodies and I am happy with both. But when I go out and I don´t know exactly what I´m up to, I take the 1DX, because it can handle more situations than the 5DIII. In some cases, good light being one, I benefit from the higher resolution of the 5DIII and I also appreciate the lower weight, when combined with the 600/4 II. I have the battery grip for it, but I very seldom use it. To me it is the perfect combination having both.
I agree Eldar, and I do exactly the same thing you do....having one of each is great for the reasons you stated.
Looking forward to a big MP to replace the 5d3....but I don't see the 1dx leaving my bag for quite some time.