Olympus SP-810 UZ has a 14.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features TruePic III+ processor. On the other hand, Sony RX10 III has a 20.0MP 1″ (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features Bionz X processor.
Sony RX10 III's sensor provides 6MP more than Olympus SP-810 UZ'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 SP-810 UZ and RX10 III sensor size comparison.
As seen above, Sony RX10 III has a 4.1x Larger sensor area than Olympus SP-810 UZ. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.