Nikon D850 has a 46.0MP Full frame (35.9 x 23.9 mm ) sized BSI-CMOS sensor and features Expeed 5 processor. On the other hand, Nikon D780 has a 25.0MP Full frame (35.9 x 23.9 mm ) sized BSI-CMOS sensor and features Expeed 6 processor.
Nikon D850's sensor provides 21MP more than Nikon D780'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 difference between these two cameras is that Nikon D850's sensor lacks anti-alias (Low-Pass) filter. 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 D850 and D780 sensor size comparison.
Nikon D850 and Nikon D780 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Nikon D780 has 86% larger pixel area (35.25µm2 vs 18.88µm2) compared to Nikon D850, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.