Sony RX1R II has a 42.0MP Full frame (35.9 x 24 mm ) sized BSI-CMOS sensor and features BIONZ X processor. On the other hand, Sony RX1 has a 24.0MP Full frame (35.8 x 23.8 mm ) sized CMOS sensor .
Sony RX1R II's sensor provides 18MP more than Sony RX1'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 difference between these two cameras is that Sony RX1R II'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 RX1R II and RX1 sensor size comparison.
Sony RX1R II and Sony RX1 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.
DxOMark Sensor Scores
Both Sony RX1R II and Sony RX1 sensors have been tested by DxoMark. DxoMark scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Of the two cameras that we are comparing, RX1R II has scored 97, 4 points higher than RX1.