Both Canon S120 and Nikon P7800 have 12.0 MP resolution sensors but Canon S120's sensor is 1/1.7" (7.44 x 5.58 mm ) and Nikon P7800's sensor is 1/1.7 (7.44 x 5.58 mm ).
Since Nikon P7800'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 Canon S120.
Below you can see the S120 and P7800 sensor size comparison.
Canon S120 and Nikon P7800 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.
DxOMark Sensor Scores
Both Canon S120 and Nikon P7800 sensors have been tested by DxoMark. DxoMark scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Of the two cameras that we are comparing, S120 has scored 56, 2 points higher than P7800.