Both Nikon P7100 and Nikon S01 have 10.0 MP resolution sensors but Nikon P7100's sensor is 1/1.7-inch (7.44 x 5.58 mm ) and Nikon S01's sensor is 1/2.9-inch (4.96 x 3.72 mm ).
Since Nikon P7100'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 S01.
Below you can see the P7100 and S01 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon P7100 and Nikon S01 Cameras
As seen above, Nikon P7100 has a 2.3x Larger sensor area than Nikon S01. 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.
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
Nikon P7100
or the
Nikon S01 ,
including hyperfocal distance.
One thing to watch when comparing these two: they have different sensor sizes
(1/1.7-inch versus 1/2.9-inch),
so compare them at the same framing rather than the same focal length.
Put the same focal length on the smaller sensor and it will show less depth of
field, not more, because it also crops tighter. The calculator shows the
full frame equivalent focal length for each body so you can match the framing.