Canon 5D MIII has a 22.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Digic 5+ processor. On the other hand, Panasonic S5 II has a 24.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Venus Engine processor.
One other difference between these two cameras that is worth mentioning is that Panasonic S5 II'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 5D MIII and S5 Mark II sensor size comparison.
Sensor Size and Resolution Comparison image of Canon 5D MIII and Panasonic S5 II Cameras
Canon 5D MIII and Panasonic S5 II have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.