Canon G1 X III has a 24.0MP APS-C (22.3 x 14.9 mm ) sized CMOS sensor and features DIGIC 7 processor. On the other hand, Sony A550 has a 14.0MP APS-C (23.4 x 15.6 mm ) sized CMOS sensor and features Bionz processor.
Canon G1 X III's sensor provides 10MP more than Sony A550'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 G1 X III and A550 sensor size comparison.
Canon G1 X III and Sony A550 have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.