Both Casio EX-10 and Panasonic 3D1 have 12.0 MP resolution sensors but Casio EX-10's sensor is 1/1.7-inch (7.44 x 5.58 mm ) and Panasonic 3D1's sensor is 1/2.3-inch (6.17 x 4.55 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 3D1.
Below you can see the EX-10 and 3D1 sensor size comparison.
As seen above, Casio EX-10 has a 1.5x Larger sensor area than Panasonic 3D1. 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.