Both Canon S110 and Nikon P7800 have 1/1.7-inch sized 12.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the S110 and P7800 sensor size comparison.
Sensor Size and Resolution Comparison image of Canon S110 and Nikon P7800 Cameras
Canon S110 and Nikon P7800 have the same 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
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It 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. Canon S110 and Nikon P7800 sensors have been tested by DxO and the results show that P7800 has a better overall score of 54, 6 points higher compared to S110's score of 48.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Canon S110
48
20.6 bits
11.2 Evs
168 ISO
Nikon P7800
54
21.2 bits
11.7 Evs
200 ISO
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Canon S110
or the
Nikon P7800 ,
including hyperfocal distance.