Both Panasonic TS6 and Fujifilm F800EXR have 16.0 MP resolution sensors but Panasonic TS6's sensor is 1/2.33' (6.08 x 4.56 mm ) and Fujifilm F800EXR's sensor is 1/2-inch (6.4 x 4.8 mm ).
Since Fujifilm F800EXR'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 TS6.
Below you can see the TS6 and F800EXR sensor size comparison.
As seen above, Fujifilm F800EXR has a 1.1x Larger sensor area than Panasonic TS6. 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.