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, Casio EX-ZR800 has a 16.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CMOS sensor and features EXILIM Engine HS 3 processor.
Below you can see the P500 and EX-ZR800 sensor size comparison.
Nikon P500 and Casio EX-ZR800 have 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 32% larger pixel area compared to Casio EX-ZR800, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.