Nikon D6 has a
21.0MP Full frame (35.9 x 23.9 mm ) sized CMOS sensor and features Expeed 6 processor. On the other hand, Nikon D3 has a
12.0MP Full frame (36 x 23.9 mm ) sized CMOS sensor and features Expeed 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 D6 and D3 sensor size comparison.
Nikon D6 and Nikon D3 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.