Both Casio EX-Z450 and Panasonic G10 have 12.0 MP resolution sensors but Casio EX-Z450's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Panasonic G10's sensor is Four Thirds (17.3 x 13 mm ).
Since Panasonic G10'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 EX-Z450.
Below you can see the EX-Z450 and G10 sensor size comparison.
As seen above, Panasonic G10 has a 8.0x Larger sensor area than Casio EX-Z450. 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.