Both Kodak Mini and Nikon S01 have 10.0 MP resolution sensors but Kodak Mini's sensor is 1/3-inch (4.8 x 3.6 mm ) and Nikon S01's sensor is 1/2.9-inch (4.96 x 3.72 mm ).
Since Nikon S01'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 Kodak Mini.
Below you can see the Mini and S01 sensor size comparison.
Kodak Mini and Nikon S01 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.