Nikon D7100 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor . 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 D7100's sensor provides 12MP 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.
Another difference between these two cameras is that Nikon D7100's sensor lacks anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the D7100 and D3 sensor size comparison.
As seen above, Nikon D3 has a 2.3x Larger sensor area than Nikon D7100. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.
DxOMark Sensor Scores
Both Nikon D7100 and Nikon D3 sensors have been tested by DxoMark. DxoMark 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. Of the two cameras that we are comparing, D7100 has scored 83, 2 points higher than D3.