Both Nikon P340 and Nikon S8100 have 12.0 MP resolution sensors but Nikon P340's sensor is 1/1.7-inch (7.44 x 5.58 mm ) and Nikon S8100's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Nikon P340'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 S8100.
Below you can see the P340 and S8100 sensor size comparison.
As seen above, Nikon P340 has a 1.5x Larger sensor area than Nikon S8100. 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.