Both Nikon S9100 and Casio EX-10 have 12.0 MP resolution sensors but Nikon S9100'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 Nikon S9100.
Below you can see the S9100 and EX-10 sensor size comparison.
As seen above, Casio EX-10 has a 1.5x Larger sensor area than Nikon S9100. 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.