Sigma fp has a 25.0MP Full frame (35.9 x 23.9 mm ) sized BSI-CMOS sensor . On the other hand, Nikon 1 V3 has a 18.0MP 1-inch (13.2 x 8.8 mm ) sized CMOS sensor and features Expeed 4A processor.
Sigma fp's sensor provides 7MP 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 fp and 1 V3 sensor size comparison.
As seen above, Sigma fp has a 7.4x 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.