Both Olympus E-M10 II and Kodak S-1 have 16.0 MP resolution sensors but Olympus E-M10 II's sensor is Four Thirds (17.3 x 13 mm ) and Kodak S-1's sensor is Four Thirds (17.3 x 13 mm ).
Since Kodak S-1'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 Olympus E-M10 II.
Below you can see the E-M10 II and S-1 sensor size comparison.
Olympus E-M10 II and Kodak S-1 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. On the other hand, since Olympus E-M10 II has 1% larger pixel area compared to Kodak S-1, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.