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, Nikon 1 J5 has a 21.0MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features Expeed 5A processor.
One other difference between these two cameras that is worth mentioning is that Nikon 1 J5's sensor doesn't have an 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 1 V3 and J5 sensor size comparison.
Nikon 1 V3 and Nikon 1 J5 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Nikon 1 V3 has 13% larger pixel area compared to Nikon 1 J5, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.
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 Nikon 1 J5 sensors have been tested by DxO and the results show that J5 has a better overall score of 65, 13 points higher compared to 1 V3's score of 52.