Canon 1D C has a
18.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Dual Digic 5+ processor. On the other hand, Sony A7R has a
36.0MP Full frame (35.9 x 24 mm ) sized CMOS sensor and features Bionz X processor.
Sony A7R's sensor provides 18MP 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.
One other difference between these two cameras that is worth mentioning is that Sony A7R's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the 1D C and A7R sensor size comparison.
Canon 1D C and Sony A7R 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.