Nikon S6100 has a 16.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features Expeed C2 processor. On the other hand, Nikon S31 has a 10.0MP 1/2.9-inch (4.96 x 3.72 mm ) sized CCD sensor .
Nikon S6100's sensor provides 6MP more than Nikon S31's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the S6100 and S31 sensor size comparison.
As seen above, Nikon S6100 has a 1.5x Larger sensor area than Nikon S31. 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.