Both Olympus SZ-30MR and Kodak S-1 have 16.0 MP resolution sensors but Olympus SZ-30MR's sensor is 1/2.3-inch (6.17 x 4.55 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 SZ-30MR.
Below you can see the SZ-30MR and S-1 sensor size comparison.
As seen above, Kodak S-1 has a 8.0x Larger sensor area than Olympus SZ-30MR. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.