From one point of view choosing something to compare to the Canon EF 400mm f2.8L IS II USM seems a little pointless, if this is the type of lens that you need then nothing else will do. There are alternatives, Nikon has an equivalent, their Nikkor 400mm f2.8G ED VR AF-S, DxOMark has not tested this yet, but you would not be looking at this lens against the Canon unless you were starting completely from scratch.
Canon actually has 3 current models of 400mm lens; the others have maximum apertures of f/4 and f/5.6. Neither of these has been tested at the time of writing but clearly they will not have the same crisp, shallow depth of field which makes these fast telephoto lenses so special, though they are very much lighter, the f/4 weighs 1940g and the f/5.6 a mere 1250g.
Canon also has an EF 300mm f2.8L IS II USM, again, the shallowness of the depth of field will not quite compare to the 400 but it will be pretty close and with a weight of just 2400g it is obviously much more manageable. The operational features of these two lenses are identical; indeed they share an instruction manual. The optical design is similar too with 16 elements in 12 groups. Both of these lenses are excellent with DxOMark scores of 30 for the 400 and 32 for the 300. Sharpness, when measured on a Canon EOS 5D Mk III is 21 P-Mpix for the 400 and 22P-Mpix for the 300, the two highest scores achieved for any lens mounted on this camera.
Drilling deeper into the scores is like looking at two sets of results from the same lens, distortion is negligible, chromatic aberration is well controlled (slightly better on the 300) and vignetting at around 1 stop when either lens is used wide open. If you want to be really picky, strictly the 300 is better, but if you need the length then the 400 is only just behind.