Fujifilm X100S has a 16.0MP APS-C (23.6 x 15.8 mm ) sized CMOS X-TRANS II sensor and features EXR II processor. On the other hand, Sony RX1R II has a 42.0MP Full frame (35.9 x 24 mm ) sized BSI-CMOS sensor and features BIONZ X processor.
Sony RX1R II's sensor provides 26MP more than Fujifilm X100S'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.
Another similarity between these two cameras is that both Sony RX1R II and Fujifilm X100S sensors lack anti-alias (Low-Pass) filters. 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 X100S and RX1R II sensor size comparison.
As seen above, Sony RX1R II has a 2.3x Larger sensor area than Fujifilm X100S. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.