Ricoh WG-6 has a 20.0MP 1/2.3" (6.17 x 4.55 mm ) sized BSI-CMOS sensor . On the other hand, Nikon S8100 has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Expeed C2 processor.
Ricoh WG-6's sensor provides 8MP more than Nikon S8100'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 WG-6 and S8100 sensor size comparison.
Ricoh WG-6 and Nikon S8100 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 Nikon S8100 has 68% larger pixel area (2.34µm2 vs 1.39µm2) compared to Ricoh WG-6, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.