Nikon 1 V1 has a
10.0MP 1-inch (13.2 x 8.8 mm ) sized CMOS sensor . On the other hand, Nikon 1 J4 has a
18.0MP 1' (13.2 x 8.8 mm ) sized CMOS sensor and features Expeed 4 processor.
Nikon 1 J4's sensor provides 8MP more than Nikon 1 V1'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 1 V1 and 1 J4 sensor size comparison.
Nikon 1 V1 and Nikon 1 J4 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. On the other hand, since Nikon 1 V1 has 81% larger pixel area compared to Nikon 1 J4, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.