Samsung NX mini has a
20.5MP 1' (13.2 x 8.8 mm ) sized BSI-CMOS sensor . 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 moiré occurring in certain scenes.
Below you can see the NX mini and J5 sensor size comparison.
Samsung NX mini and Nikon 1 J5 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.