With the 5DMKIII Canon have caught up in most areas with Nikon regarding handling, AF, features.
With respect to the the cameras only the D800 has a clear advantage with its sensor, even ignoring the resolution difference the D800 has better noise performance and more importantly the dynamic range difference is HUGE. How important that is to you depends on your style and what you shoot, but DR is one of the biggest limits of modern DSLR cameras and is one of the sole reason why some people still use film (esp. B&W).
The DR difference is the real deal break to me, and it is not just that the D800 has great DR (which is does, best there is), it is that the 5DMKIII is deficient, like most recent canon sensors. Canon used to lead the world with the highest DR figures around but they seemingly haven't made any progress since then. It is now at the point where new Sony crop sensors are outperforming Canon full frame sensors! If you shoot any high contrast scnes then this will really be one of the main deciding factors, if you shoot in cotnrolled studio lighting you wont care.
You should also look at what lenses you want:
If you must have an 85mm f1.2L then Canon it is, although I suggest you really try the marginally optically superior Nikon 85mm f/1.4G and decide if the 1/3rd stop makes a big difference (the 1/3rd stop difference will be negated by the D800 noise performance, will the DOf difference be important?).
Canon have nothing at all to compare with the Nikon 14-24mm f/2.8. For landscape/cityscape/seascapes Canon just cannot compete at the moment taking into account lenses and sensor differences. Canon landscape togs were already mounting the Nikon 14-24 on their canon 5dMKII and enjoyed afford high resolution body (those with money already swapped to the D3x to get a better sensor). This time round Canon have given nothing to the landscape photographers and so many are jumping ship to the D800.
A typical setup might be the 24-70mm f/2.8 and 70-200mm f2.8, these turn out to be significantly cheaper on Nikon. The older Canon 24-70 is just not comparable image quality wise.
For wildlife the exotic Nikon tele primes are far, far cheaper. The Nikon 200-400 f/4.0 has been around since the 1980s and Canon hasn't released theirs yet. On the flip-side you might find some cheaper older canon exotics *but there are also cheaper 2nd hand Nikon exotics, going back 50 years if you so wish).
Canon do have cheap 2nd hand 24mm and 35mm f/1.4 primes to be found at the moment. Some people will go for a 24, 35 and 85mm prime setup, you could save money on Canon here.
Conversely, nikon have now got some amazing 1.8G primes that compete with both manufactures 1.4 primes, both optically and AF wise.
Canon have a 17mm TS lens which is wonderful, Nikon haven't even announced a similar lens. In general the Canon TS lenses are slightly better to use, optically all very similar.
Some other things to consider:
The D800 is cheaper and presents much better value for money at the moment.the 5DMKII is clearly over priced. The D800 has a few extra builtin features like the flash which can be useful in emergencies or used as a trigger.
The D800 has a RAW HDMI output for video, if you take video seriously then the D800 is a clear winner due to this (although if video is really you thing you might want to swap out the AA filter for something stronger).
The D800 can mount crop lenses and allow them to be run in either DX mode, 1.2 crop or Full Frame. The F-mount is compatible with 50-55 years worth of lens, some of them are golden and still work flawlessly today. In general Nikon are very keen on backwards and forwards compatibility.
The Nikon D800 production seems to have been marred by some AF calibration issues, this is reportedly fixed but I would be careful buying old stock lenses. Real shame, prevents Nikon having a perfect product release. Conversely, the 5DMKII has a light leak issue, but it is fairly mundane.
The 5DMKIII is a little faster, 6FPS vs 4FPS. With the D800 you can simply plop it into 1.2 crop mode and get 24MP images at 5FPS, 6PFS is possible in DX mode. the 5FPS in 1.2x crop mode is very nice actually because in general when high speed is needed, e.g. during sports and some wildlife, you will likely be cropping or needing the extra reach anyway, 24MP is still plenty to work with. More important than stated FPS is how the AF keeps up, read-write speeds to the card, etc. Here I have heard amazing stores about the D800 (don;t know about the 5DMKIII). Bottom line is most people will be perfectly happy with 4FPS if they can rely on the AF and that is preferably to 6-12FPS with less reliable results. I know some pros shoot Nikon and Canon pro bodies at the lower frame rates on purpose to improve their chances of getting the key shots rather than machine gunning and hoping. Neither cameras are sports cameras, you need to go for 1dX or D4 if this is your ultimate goal.
I have heard the D800 metering is more accurate, not read enough to be sure.
Nikon changed the LCDs to have closer to sRGB output, some people don't like the cooler colours displayed. This can be mostly corrected in the menus.
Canon's liveview is in general better implemented, but I hear Nikons liveview autofocus is better, especially in low light.
