The "element" you mention is called pixel.
- The D4s sensor has 16,163,840 pixels (= 16.16 mpix), and each individual pixel has a pitch of 7.3 µm (49% larger than the D810 pixel).
- The D810 sensor has 36,152,320 pixels (= 36.15 mpix), and each individual pixel has a pitch of 4.9 µm (33% smaller than the D4s pixel).
That means that the original image capture by the D4s has much less resolution, information, and more light captured by each individual pixel (hence less noise at 1:1 level). And the original image capture by the D810 has much more resolution, information, and less light captured by each individual pixel.
However, you can easily resize the 36 mpix image produced by the D810 to a smaller 16 mpix image. This will mimic the same resolution, information and light levels of the D4s, while the opposite will be much harder to accomplish (it's 'impossible' to convert the 16 mipx D4s image into a 36 mpix image without distorting it).
This allows the D810 sensor to capture much more detail, and you can be much more flexible with the file for printing, resizing, cropping etc., with better sharpness, dynamic range, color management etc., but you need to post-process the D810 file later. It gives you much more flexibility and versatility. On the other hand, the D4s file allows you to be faster, with minimum post-processing, with lighter files, and better noise, easier to manage right out of the camera.
But the D810 also has the sRAW format too (the small RAW "cooked" file), that mimics the effect of each square segment of four D810 pixels to collect light as they were only one single pixel instead. That produces a "cooked" RAW file with four times less megapixels, with a resolution of 3,680 x 2,456 pixels (9,038,080 pixels = 9.04 mpix). That mimics a sensor where each individual pixel has a pitch of 9.8 µm (100% larger than the D810 original pixel, and 34% larger than the D4s pixel).
That gives the D810 an extra advantage. Although this is just a software cooking process to combine each four pixels into one, it does impact the noise for the better (for the cases when you need a faster post-processing). You'd get a similar result by resizing the file later, in post, but the output would not be RAW/NEF format as the D810 camera offers you. Despite criticism out there, my results with the sRAW are just good. It is nice to have both RAW and sRAW as options, for when needed.
More info on the D810 sRAW feature:
The D4s also offers its own sRAW file too, but producing a sRAW file of only 4 mpix. Because of that, I believe the sRAW file is much more useful for the high resolution D810, than for the low resolution D4s.
So, if you need to shoot fast (photo jounalism, sports, night photos, fast post-processing, etc.), the D4s will be better. If you don't need to go fast, the D810 will offer much more, for much less $$.