Canon 5D MIII has a 22.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Digic 5+ processor. On the other hand, Nikon D810A has a 36.0MP Full frame (35.9 x 24 mm ) sized CMOS sensor and features EXPEED 4 processor. Nikon D810A's sensor provides 14MP more than Canon 5D 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 5D MIII and D810A sensor size comparison.
Canon 5D MIII and Nikon D810A 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.