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, Canon 1100D has a
12.0MP APS-C (22.2 x 14.8 mm ) sized CMOS sensor and features Digic 4 processor.
Canon G1 X III's sensor provides 12MP more than Canon 1100D'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 1100D sensor size comparison.
Canon G1 X III and Canon 1100D 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.