Nikon 1 V3 has a 18.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor and features Expeed 4A processor. On the other hand, Sony A99 has a 24.0MP Full frame (35.8 x 23.8 mm ) sized CMOS sensor and features Bionz processor.
Sony A99's sensor provides 6MP more than Nikon 1 V3'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 1 V3 and A99 sensor size comparison.
As seen above, Sony A99 has a 7.3x Larger sensor area than Nikon 1 V3. 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
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 1 V3 and Sony A99 sensors have been tested by DxO and the results show that A99 has a better overall score of 89, 37 points higher compared to 1 V3's score of 52.