Both Nikon S6500 and Nikon S7000 have 16.0 MP resolution sensors but Nikon S6500's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Nikon S7000's sensor is 1/2.3 (6.17 x 4.55 mm ).
Since Nikon S7000'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 S6500.
Below you can see the S6500 and S7000 sensor size comparison.
Nikon S6500 and Nikon S7000 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.