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Why crop if you do not need to ? Storage is cheap enough that any decent, modern computer will cope ok with the bigger raw files. Those bigger FX (full frame) files give you at least two key advantages over the cropped versions:
- more room for looser framing without loss of pixels on the subject, in case the subject moves or changes shape by standing, stretching, whatever.
- if you're close enough or can use a longer focal length you can have more pixels on your subject.
Note that we are not considering an FX sensor with one pixel density vs a DX sensor with another pixel density - there is no "reach" advantage at all. Instead this is all about using exactly the same sensor with exactly the same pixel density and pixel performance, and simply discarding part of the image. I'd much rather crop afterwards in processing than at the time of shooting in case the scene / subject changes enough that I miss something.
The whole AF sensor grid system covers the DX area, which is a 1.5 FOVCF vs the "1.3" or 1.26 FOVCF that you're used to on a 1D4. It fills the cropped area considerably.
On my camera the viewfinder covers the original FX image area but the cropped area is darkened so that you can see it but it is not as prominent as the part of the image that will be kept.
Except for possible data processing advantages leading to a faster frame rate there is no shooting or IQ advantage to using the smaller crop. However, if you manage to fill the FX area with the subject then you have the potential for downsizing the final image and gaining some image quality improvements by reducing noise. Even so, that may or may not be as good as using a better sensor with fewer pixels, such as on the D4 or D3s. Too early to tell for sure.
I doubt that the frame rate advantage is good enough to risk losing some key action if you're caught out using the cropped mode.
You may or may not like using a 36Mpx image for everything. You might find that in poor light a sensor with fewer pixels and more dynamic range (less noise and better colour) could be more useful. At other times you will love the detail from the higher pixel count and/or higher pixel density. If you shoot at large apertures you win but if you want or need to shoot at smaller apertures for the DOF then you will find that diffraction robs you of some or all of that pixel density advantage compared with using a more optimal aperture. e.g. at f/16 or even f/11 you might be less impressed with the pixel density than at f/4. You won't be any worse off than using a sensor with fewer pixels but you'll be disproportionately worse off than you were at the larger apertures.
Also, read the reviews for yourself (e.g. at www.bythom.com) but you might find that the acuity of the 200-400 at long shooting distances is not as good as you'd be getting from your Canon 500 f/4 or from the same 200-400 at shorter distances. That might sound worse than it really is because at those longer distances the wildlife is probably too small to make a great photo anyway. The lens does not perform greatly with TCs and so the f/8 AF capability of the D800 or D4 is somewhat wasted on that lens. On the other hand, the high pixel density of the D800 is equivalent to having a TC on the lens without the loss of light or aperture.
My guess is that you'll like the D800 better than your 1D4 in terms of the AF system performance and the ability to use auto ISO plus exposure compensation in M mode, giving you full control of both DOF and subject blur but still having automatic exposure. I don't know what the DR will be like but I suspect the D4 will be better in that regard than the 1D4 or the D800, making it a better low-light camera (assuming it is as good as the D3s if not better).
A switch to Nikon is expensive and has pros and cons. Running both systems has other problems in terms of usability, accessories, etc. I'm sure that you should carefully consider the 1Dx before switching brands.
I got into Nikon at a time when Canon was giving me a hard time with camera defects and poor servicing. Had my cameras been ok I would not have any Nikon gear and would not be driven to throw a lot of money at it. The 14-24 and especially the 200-400 are expensive lenses.
 I've not seen any reviews of how well the 200-400 works at high pixel density such as on the D800 or the older D7000. It's great at 12 Mpx.