It would be helpful if someone were to list all the essential features that are exclusive to each camera, and by essential I mean features excluding personal idiosyncrasies, likes and dislikes related to ergonomics, menu arrangement, button positions, and general handling.
For example, we know that the D800 has higher resolution and better DR to a degree which is significant if the print is large enough and if the scene is of sufficiently high contrast. There's no doubt about that.
We know that the 5D3 has a higher frame rate of 6fps instead the 4fps of the D800. Clearly this is of significance in certain circumstances, shooting fast-moving subjects for example. On the other hand this advantage of the 5D3 is somewhat mitigated by the fact that one can also get 6fps with the D800 by lowering resolution to DX mode, which is 15mp. The D800 in those circumstances then hands over the resolution advantage to ther 5D3, but in doing so the D800 creates an additional advantage, in certain circumstances, which is often attributed to the cropped format, namely the longer reach with a given lens.
For example, let's consider the scenario of two photographers out shooting wildlife, both carrying a 400mm lens but one photogrpher using a 5D3 and the other a D800. A rare species of bird flies by. Both photographers raise their camera in auto-tracking and continuous mode. The 5D3 owner thinks to himself, I'll get better shots than my colleague because I can use 6fps. However, the D800 owner switches to DX mode and effectively gets a 600mm lens as well as 6fps.
Now which camera is likely to produce the sharper and more detailed shots of the bird, viewed at equal magnification on monitor or print?
I've seen it mentioned that the 5D3 LiveView feature is easier to use for manual focussing, but there's so much confusion on this issue it's difficult to know whether the 5D3 has a real advantage in this respect, or whether the problem is due to the D800 simply having an additional feature of 'exposure simulation mode' whereby the light being projected on the D800 LiveView screen is limited by the size of the aperture selected, requiring one to set the lens to maximum aperture for maximum brightness, which is no big deal.
The other source of confusion here is the fact that the D800 allows for greater magnification of the LiveView image, 23x as opposed to 10x for the 5D3, so any comparison of LiveView image clarity should be at equal magnification to avoid confusion.
Nevertheless, the LiveView monitor on my Canon 50D does
produce a consistently brighter image than my D800E (I've just compared it as I write this, after setting the D800's monitor brightness to its maximum of +5), so I would have to concede that it is very likely that the 5D3 really does have a more useful LiveView monitor for critical focussing of dark or poorly lit scenes.
Since I don't own a 5D3 and haven't even explored all the features of my D800E yet, there may well be other significant features exclusive to each camera. For example, I believe the range of shutter speeds that can be set when autobracketing ISO is more useful on the D800.