Both Panasonic ZS1 and Nikon S01 have 10.0 MP resolution sensors but Panasonic ZS1's sensor is 1/2.5-inch (5.744 x 4.308 mm ) and Nikon S01's sensor is 1/2.9-inch (4.96 x 3.72 mm ).
Since Panasonic ZS1'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 ZS1 and S01 sensor size comparison.
As seen above, Panasonic ZS1 has a 1.3x 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.