Nikon D810 has a 36.0MP Full frame (35.9 x 24 mm ) sized CMOS sensor and features EXPEED 4 processor. On the other hand, Nikon D850 has a 46.0MP Full frame (35.9 x 23.9 mm ) sized BSI-CMOS sensor and features Expeed 5 processor. Nikon D850's sensor provides 10MP more than Nikon D810's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Another similarity between these two cameras is that both Nikon D850 and Nikon D810 sensors lack anti-alias (Low-Pass) filters. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the D810 and D850 sensor size comparison.
Nikon D810 and Nikon D850 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.