I've had my D800E since the beginning of July, and here are a few unscientific observations I've made...
Dynamic Range - the 5D Mark III has a bit more dynamic range straight out of the camera, but the D800E files give you a whole lot more dynamic range to work with if you want to spend the extra time in post-processing.
Image Sharpness/Acuity - it's close, but I would give this one to the 5D Mark III if it were not for the lower pixel count; the amount of fine detail sharpness and resolution is better in the Canon files, but the Nikon file has 28% more real estate which helps it when you make larger prints (24 x 36"). I really expected to see better sharpness with no AA filter in the D800E, and Canon seems to be getting better performance out of their lenses with the new lens correction profiles loaded into the 5D mark III, so this comparison might surprise a lot of people.
Focusing - the 5D mark III is vastly superior in AF speed and, more importantly, in accuracy. The D800E isn't bad - it's about the same as the D700, but the Canon is in a different league altogether.
Metering - I would call it a draw... both cameras are pretty good, but neither one is perfect.
High ISO Noise - I have no idea - I normally shoot at ISO 100.