Sony RX10 II has a 20.0MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features Bionz X processor. 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.
Another difference between these two cameras is that Nikon 1 J5's sensor lacks 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 moire occurring in certain scenes.
Below you can see the RX10 II and J5 sensor size comparison.
Sony RX10 II and Nikon 1 J5 sensors have exactly the same size so none of them has any advantage over other in this area.