Sony A7 III has a
24.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz X processor. On the other hand, Canon 1D C has a
18.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Dual Digic 5+ processor.
Sony A7 III's sensor provides 6MP more than Canon 1D C'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 A7 III and 1D C sensor size comparison.
Sony A7 III and Canon 1D C 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.