Sony A6300 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features BIONZ X processor. On the other hand, Nikon 1 V3 has a 18.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor and features Expeed 4A processor.
Sony A6300'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 A6300 and 1 V3 sensor size comparison.
As seen above, Sony A6300 has a 3.2x 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
Both Sony A6300 and Nikon 1 V3 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, A6300 has scored 85, 33 points higher than 1 V3.