Both Casio TRYX and Panasonic G2 have 12.0 MP resolution sensors but Casio TRYX's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Panasonic G2's sensor is Four Thirds (17.3 x 13 mm ).
Since Panasonic G2'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 TRYX.
Below you can see the TRYX and G2 sensor size comparison.
As seen above, Panasonic G2 has a 8.0x Larger sensor area than Casio TRYX. 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.