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, Pentax K-3 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Prime III processor.
Pentax K-3's sensor provides 12MP 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.
One other difference between these two cameras that is worth mentioning is that Pentax K-3's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the P500 and K-3 sensor size comparison.
![Nikon P500 vs Pentax K-3 Sensor Size Comparison]()
Sensor Size and Resolution Comparison image of Nikon P500 and Pentax K-3 Cameras
As seen above, Pentax K-3 has a 13.1x Larger sensor area than Nikon P500. 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.