Nikon D3 has a 12.0MP Full frame (36 x 23.9 mm ) sized CMOS sensor and features Expeed processor. On the other hand, Nikon D6 has a 21.0MP Full frame (35.9 x 23.9 mm ) sized CMOS sensor and features Expeed 6 processor.
Nikon D6's sensor provides 9MP more than Nikon D3'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 D3 and D6 sensor size comparison.
![Nikon D3 vs Nikon D6 Sensor Size Comparison]()
Sensor Size and Resolution Comparison image of Nikon D3 and Nikon D6 Cameras
Nikon D3 and Nikon D6 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.