Sony HX20V has a 18.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features BIONZ processor. On the other hand, Olympus XZ-10 has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor .
Sony HX20V's sensor provides 6MP more than Olympus XZ-10'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 HX20V and XZ-10 sensor size comparison.
Sony HX20V and Olympus XZ-10 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 Olympus XZ-10 has 52% larger pixel area (2.38µm2 vs 1.56µm2) compared to Sony HX20V, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.