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I have read through, I'm sure, dozens of 7D vs. 1D Mark III threads in the last couple of years. In every one of them, the split between those whose favor one camera over the other seems to be fairly even. I think that the reason is that they are both excellent cameras with good capabilities, but each of them has capabilities that are better suited to specific shooting than are the capabilities of the other.
I owned both the 7D and the 1D Mark III, and my ownership of those bodies was simultaneous for about 6 months. My assessment is that the 1D Mark III produces beautiful files. It has a very capable AF system, and it is hard to beat the feel of the build quality of a 1-series body. The 7D, with its high pixel density, is a camera that can't be beaten by any camera when shooting is likely to be done in focal length-limited situations. It also has a very capable AF system. In real world shooting of moving wildlife, flying birds, etc., my in-focus rates with the two bodies were so close that I'm not sure which one gave me more success, and I can't recall a single instance where my failure to get a shot was the result of the AF system of either camera failing me.
With regard to noise, there is no question that the 7D files are noisier than those of the 1D Mark III at the pixel level, but the 7D has almost twice as many pixels as does the 1D Mark III, and, at the whole image level, noise is actually very similar. Further, even at the pixel level, if you downscale 7D files to the 10 MP of the 1D Mark III or if you upscale the 1D Mark III files to the 18 MP of the 7D, noise is quite similar. Thus, in focal length-limited situations where cropping is a necessity and where the 1D Mark III files are going to have to be upscaled, any noise advantage that the 1D Mark III may start out with at the pixel level is going to disappear.
For me, the bottom line is that, if was going to be shooting in focal length-limited situations or if I wanted enough pixels to be able to make larger prints, the 7D would be my pick. If I was only very rarely shooting in focal length-limited situations, if I only rarely needed to crop severely, and if I was interested only in making prints at moderate sizes, I'd probably pick the 1D Mark III. Further, while each of these cameras his its advantages, neither is the winner in all situations over the other.