Both Ricoh GXR Mount A12 and Sony W510 have 12.0 MP resolution sensors but Ricoh GXR Mount A12's sensor is APS-C (23.6 x 15.7 mm ) and Sony W510's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Ricoh GXR Mount A12'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 Sony W510.
Below you can see the GXR Mount A12 and W510 sensor size comparison.
As seen above, Ricoh GXR Mount A12 has a 13.2x Larger sensor area than Sony W510. 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.