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