Samsung NX mini has a 20.5MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor . On the other hand, Nikon 1 J3 has a 14.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor . Samsung NX mini's sensor provides 6.5MP more than Nikon 1 J3's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the NX mini and 1 J3 sensor size comparison.
Samsung NX mini 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 J3 has 40% larger pixel area (8.20µm2 vs 5.82µm2) compared to Samsung NX mini, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.