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 D3X has a 25.0MP Full frame (35.9 x 24 mm ) sized CMOS sensor and features Expeed processor.
Nikon D3X's sensor provides 13MP 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 D3X sensor size comparison.
Nikon D3 and Nikon D3X 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. Nikon D3 and Nikon D3X sensors have been tested by DxO and the results show that D3X has a better overall score of 88, 7 points higher compared to D3's score of 81.