Both Nikon S6500 and Panasonic SZ10 have 16.0 MP resolution sensors but Nikon S6500's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Panasonic SZ10's sensor is 1/2.33' (6.08 x 4.56 mm ).
Since Nikon S6500'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 SZ10.
Below you can see the S6500 and SZ10 sensor size comparison.
Nikon S6500 and Panasonic SZ10 have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.