Both Nikon P7800 and Ricoh GXR A12 50mm have 12.0 MP resolution sensors but Nikon P7800's sensor is 1/1.7-inch (7.44 x 5.58 mm ) and Ricoh GXR A12 50mm's sensor is APS-C (23.6 x 15.7 mm ).
Since Ricoh GXR A12 50mm'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 P7800.
Below you can see the P7800 and GXR A12 50mm F2.5 Macro sensor size comparison.
As seen above, Ricoh GXR A12 50mm has a 8.9x Larger sensor area than Nikon P7800. 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.