Nikon D500 has a
21.0MP APS-C (23.5 x 15.7 mm ) sized CMOS sensor and features Expeed 5 processor. On the other hand, Pentax K-3 III Monochrome has a
26.0MP APS-C (23 x 15.5 mm ) sized CMOS sensor and features PRIME V processor.
Pentax K-3 III Monochrome's sensor provides 5MP more than Nikon D500'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.
Another similarity between these two cameras is that both Pentax K-3 III Monochrome and Nikon D500 sensors lack anti-alias (Low-Pass) filters. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the D500 and K-3 III Monochrome sensor size comparison.
Nikon D500 and Pentax K-3 III Monochrome have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.