Samsung HZ50W has a 14.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor . On the other hand, Sony RX10 has a 20.0MP 1-inch (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features Bionz X processor.
Sony RX10's sensor provides 6MP more than Samsung HZ50W'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 HZ50W and RX10 sensor size comparison.
As seen above, Sony RX10 has a 4.2x Larger sensor area than Samsung HZ50W. 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.