Both Panasonic G6 and Panasonic G7 have 16.0 MP resolution sensors but Panasonic G6's sensor is Four Thirds (17.3 x 13 mm ) and Panasonic G7's sensor is Four Thirds (17.3 x 13 mm ).
Since Panasonic G7'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 G6.
Below you can see the G6 and G7 sensor size comparison.
Panasonic G6 and Panasonic G7 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.