Nikon D810A has a
36.0MP Full frame (35.9 x 24 mm ) sized CMOS sensor and features EXPEED 4 processor. On the other hand, Canon 1Ds MIII has a
21.0MP Full frame (36 x 24 mm ) sized CMOS sensor .
Nikon D810A's sensor provides 15MP more than Canon 1Ds MIII'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.
Below you can see the D810A and 1Ds MIII sensor size comparison.
Nikon D810A and Canon 1Ds MIII have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.