Both Panasonic ZS1 and Fujifilm Z35 have 10.0 MP resolution sensors but Panasonic ZS1's sensor is 1/2.5-inch (5.744 x 4.308 mm ) and Fujifilm Z35's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Fujifilm Z35'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 ZS1.
Below you can see the ZS1 and Z35 sensor size comparison.
As seen above, Fujifilm Z35 has a 1.1x Larger sensor area than Panasonic ZS1. 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.