Both Panasonic ZS3 and Nikon P7100 have 10.0 MP resolution sensors but Panasonic ZS3's sensor is 1/2.3-inch (6.08 x 4.56 mm ) and Nikon P7100's sensor is 1/1.7-inch (7.44 x 5.58 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 Panasonic ZS3.
Below you can see the ZS3 and P7100 sensor size comparison.
As seen above, Nikon P7100 has a 1.5x Larger sensor area than Panasonic ZS3. 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.