Both Nikon P7800 and Olympus XZ-2 iHS have 12.0 MP resolution sensors but Nikon P7800's sensor is 1/1.7 (7.44 x 5.58 mm ) and Olympus XZ-2 iHS's sensor is 1/1.7" (7.44 x 5.58 mm ).
Since Olympus XZ-2 iHS'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 XZ-2 iHS sensor size comparison.
Nikon P7800 and Olympus XZ-2 iHS 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 Nikon P7800 and Olympus XZ-2 iHS 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, P7800 has scored 54, 5 points higher than XZ-2 iHS.