I've got both the 1Ds III and 1D X right now, and have done some comparison tests for both low ISO noise, resolution, and dynamic range. I also did the same comparisons with the 1D X and a friends D800E.
I'd say the resolution difference between the Canon's is very, very close. The 1Ds III might pull a slight amount of detail more than the 1D X, but only 3 megapixels is a very small difference. On a huge print you might notice it if they were side by side, but honestly the 1D X could make most any print that the 1Ds III could. A fair way to look at is the 7% linear difference. If you can make a 48 inch wide print with the 1Ds III, then you could make a 45 inch wide print with the 1D X. The D800E obviously eats them both for lunch with 36 megapixels.
On low ISO dynamic range, I'd give a slight edge to the 1D X over the 1Ds III. Both have a fair bit of leeway to push the shadows, but the 1D X holds off pattern noise just a tiny bit better than the 1Ds III, maybe 1/2 stop? The pattern noise in the 1Ds III is horizontal and the 1D X is vertical. The 1D X noise is just a little less objectionable (finer) before a pattern becomes evident as the shadows get pushed. Both do better when you are pushing shadows that are not totally black. The 1Ds III seemed to hold highlight detail just a tiny bit better at equivalent exposures, a little less than 1/3 stop if I had to guess. D800E again eats them both for lunch in terms of low ISO shadow noise. Just cleaner overall, and far deeper into underexposed blacks. I agree with Josh about preferring the default look of a pushed 1D X file over the D800E though. The tone curve of the D800E gets flat and funky looking when pushed, while the Canon keeps a more natural look to it. Nothing that couldn't be fixed in post for the Nikon, but getting a nice image is simpler with the 1D X.
Rendition between the 1Ds III and 1D X is slightly different, but both look great IMHO. Really nice look straight out of camera, great white balance and exposures. I might give the "look" edge to the 1D X. No real dramatic differences here.
Generally my take is that I don't really feel like I've given up anything by going from the 1Ds III to the 1D X, even at base ISO. And taking into consideration the speed, AF, frame rate and high ISO (oh man the high ISO!), the 1D X is just much better as an image capturing device.