Both Nikon 1 V1 and Nikon 1 J2 have 1-inch sized 10.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the 1 V1 and 1 J2 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon 1 V1 and Nikon 1 J2 Cameras
Nikon 1 V1 and Nikon 1 J2 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.
DxOMark Sensor Scores
At Camera Decision, we also look at Dxo Mark sensors when available as we think it is a good indicator of image quality.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Nikon 1 V1
54
21.3 bits
11.0 Evs
346 ISO
Nikon 1 J2
54
21.3 bits
10.8 Evs
363 ISO
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Nikon 1 V1
or the
Nikon 1 J2 ,
including hyperfocal distance.