Both Nikon S30 and Nikon S31 have 10.0 MP resolution sensors but Nikon S30's sensor is 1/3-inch (4.8 x 3.6 mm ) and Nikon S31's sensor is 1/2.9-inch (4.96 x 3.72 mm ).
Since Nikon S31'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 S30.
Below you can see the S30 and S31 sensor size comparison.
Nikon S30 and Nikon S31 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.