Ricoh G900 has a 20.0MP 1/2.3 (6.17 x 4.55 mm ) sized BSI-CMOS sensor . On the other hand, Casio TRYX has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Exilim Engine HS processor.
Ricoh G900's sensor provides 8MP more than Casio TRYX'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 G900 and TRYX sensor size comparison.
Ricoh G900 and Casio TRYX 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 Casio TRYX has 68% larger pixel area (2.34µm2 vs 1.39µm2) compared to Ricoh G900, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.