Nikon P500 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 HX10V has a 18.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features BIONZ processor.
Sony HX10V's sensor provides 6MP more than Nikon P500'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 P500 and HX10V sensor size comparison.
Nikon P500 and Sony HX10V have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Nikon P500 has 49% larger pixel area compared to Sony HX10V, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.