Ricoh WG-6 has a 20.0MP 1/2.3" (6.17 x 4.55 mm ) sized BSI-CMOS sensor . On the other hand, Sony W610 has a 14.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features BIONZ processor.
Ricoh WG-6's sensor provides 6MP more than Sony W610'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 W610 sensor size comparison.
Ricoh WG-6 and Sony W610 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 Sony W610 has 44% larger pixel area (2.01µm2 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.