Both Casio EX-Z450 and Olympus XZ-2 iHS have 12.0 MP resolution sensors but Casio EX-Z450's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Olympus XZ-2 iHS's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Olympus XZ-2 iHS'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 XZ-2 iHS sensor size comparison.
As seen above, Olympus XZ-2 iHS has a 1.5x 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.