Both Nikon P7800 and Casio TRYX have 12.0 MP resolution sensors but Nikon P7800's sensor is 1/1.7-inch (7.44 x 5.58 mm ) and Casio TRYX's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Nikon P7800's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Casio TRYX.
Below you can see the P7800 and TRYX sensor size comparison.
As seen above, Nikon P7800 has a 1.5x Larger sensor area than Casio TRYX. 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.