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 60D has a 18.0MP APS-C (22.3 x 14.9 mm ) sized CMOS sensor and features Digic 4 processor.
Canon G1 X III's sensor provides 6MP more than Canon 60D'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 60D sensor size comparison.
Canon G1 X III and Canon 60D 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 Canon 60D has 33% larger pixel area (18.54µm2 vs 13.84µm2) compared to Canon G1 X III, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.