Nikon 1 J1 has a 10.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor . On the other hand, Nikon 1 J3 has a 14.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor .
Below you can see the 1 J1 and 1 J3 sensor size comparison.
Nikon 1 J1 and Nikon 1 J3 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 J1 has 41% larger pixel area compared to Nikon 1 J3, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.