Sony RX100 II has a 20.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor . On the other hand, Olympus 1 has a 12.0MP 1/1.7" (7.44 x 5.58 mm ) sized BSI-CMOS sensor and features TruePic VI processor. Sony RX100 II's sensor provides 8MP more than Olympus 1'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 RX100 II and 1 sensor size comparison.
As seen above, Sony RX100 II has a 2.8x Larger sensor area than Olympus 1. 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.