Panasonic LX100 has a 13.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine processor. On the other hand, Sony RX1 has a 24.0MP Full frame (35.8 x 23.8 mm ) sized CMOS sensor . Sony RX1's sensor provides 11MP more than Panasonic LX100'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 LX100 and RX1 sensor size comparison.
As seen above, Sony RX1 has a 3.8x Larger sensor area than Panasonic LX100. 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.