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, Ricoh CX6 has a 10.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CMOS sensor and features Smooth Imaging Engine IV processor.
Nikon S6100's sensor provides 6MP more than Ricoh CX6'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 CX6 sensor size comparison.
Nikon S6100 and Ricoh CX6 have 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 Ricoh CX6 has 59% larger pixel area (2.81µm2 vs 1.76µm2) compared to Nikon S6100, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.