Nikon P300 has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Expeed C2 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 12MP more than Nikon P300'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 P300 and RX1 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon P300 and Sony RX1 Cameras
As seen above, Sony RX1 has a 30.4x Larger sensor area than Nikon P300. 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.