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 V2 has a 14.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor and features Expeed 3A processor.
Below you can see the 1 V3 and 1 V2 sensor size comparison.
Nikon 1 V3 and Nikon 1 V2 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 V2 has 28% larger pixel area (8.20µm2 vs 6.36µm2) compared to Nikon 1 V3, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.