I probably have the least experience with a 1D... so take this as advice with limited experience.

This last weekend, I was taking pictures of birds with a 1DX, a 100-400mm L, and a 1.4X II. What I found is the 1DX would focus for most stationalry things, but when I was trying to get birds in flight (and fill the frame), the bird did not hold position long enough for me to lock in focus with the 1.4X II attached, but worked great without the 1.4X II. The bird would either get out of range, or out of frame before it ever got locked in on focus. I got frustrated with the 1.4X II and removed it.

I was trying it out on seagulls that were close by (within 10-20 ft) with water (slight chop) back ground; they were flying past as I panned; or they were hovering as they drop down for a landing... fast moving ducks were out of the question. I was in Servo mode, IS set to 2. I do not think I ever got a shot off because there was to much movement to get it to lock in. After taking off the 1.4X II, I did not have a problem.

What I am trying to get across is the focusing ability is noticeably slower, and to the point of unacceptable when you have something coming in an out of frame quickly... that is, the camera took to long to lock on focus in that situation. This was with a 1.4xII and not the III... but I do not know if the III is actually faster. I understand the version III has better IQ, but I am not sure of its ability to focus faster.

For most cases it is going to be OK, but if you are looking to get quick focus of erratic movement, you may be disappointed. The 1.4X II and 100-400mm combination is not the best, but I do not know what you would be shooting with either.

So all this depends on your usage, and I would assume it varies greatly with the lens you use as well.