Canon 1Ds MIII has a 21.0MP Full frame (36 x 24 mm ) sized CMOS sensor . On the other hand, Nikon D4 has a 16.0MP Full frame (36 x 23.9 mm ) sized CMOS sensor and features Expeed 3 processor.
Canon 1Ds MIII's sensor provides 5MP more than Nikon D4'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 1Ds MIII and D4 sensor size comparison.
Canon 1Ds MIII and Nikon D4 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.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Canon 1Ds MIII and Nikon D4 sensors have been tested by DxO and the results show that D4 has a better overall score of 89, 9 points higher compared to 1Ds MIII's score of 80.