Both Panasonic ZS100 and Sony QX100 have 20.0 MP resolution sensors but Panasonic ZS100's sensor is 1″ (13.2 x 8.8 mm ) and Sony QX100's sensor is 1-inch (13.2 x 8.8 mm ).
Since Sony QX100'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 ZS100.
Below you can see the ZS100 and QX100 sensor size comparison.
Panasonic ZS100 and Sony QX100 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.