Nikon 1 J3 has a 14.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor . On the other hand, Nikon 1 J2 has a 10.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor and features Expeed 3 processor.
Below you can see the 1 J3 and 1 J2 sensor size comparison.
Nikon 1 J3 and Nikon 1 J2 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 J2 has 41% larger pixel area (11.57µm2 vs 8.20µm2) compared to Nikon 1 J3, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.