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I have not used either the 5D Mark III or the 1DX, but I do have a 7D, which has the zone focus option, and a 1D Mark IV, which has what is called an area focus option similar to zone focus.
With both of those bodies, my preferred focus option in most situations is still a single manually selected focus point expanded to surrounding points, and, if the background is especially busy, I'll limit the focus to just the single manually selected point. Even though the 7D zone focus and 1D Mark IV area focus both seem to work better than the auto selection options on the 1D Mark II or 1D Mark III, my experience is still that, given enough opportunities, they will still eventually let me down. Thus, I still trust my ability to keep the focus point on the subject more than I trust the camera's ability to guess correctly what the subject on which I want the camera to focus is.
Perhaps, if I spent more time experimenting with the 7D zone focus and 1D Mark IV area focus, I might know better just why they seem to work well in sometimes and why they fail in other times, but I pretty much gave up on those options and have been more than happy with the results I get using, depending on the situation, either a single manually selected point point, or a manually selected point expanded to surrounding points.