Both Panasonic ZS15 and Casio EX-10 have 12.0 MP resolution sensors but Panasonic ZS15's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Casio EX-10's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Casio EX-10'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 Panasonic ZS15.
Below you can see the ZS15 and EX-10 sensor size comparison.
As seen above, Casio EX-10 has a 1.5x Larger sensor area than Panasonic ZS15. 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.