Sony A9 has a 24.0MP Full frame (35.6 x 23.8 mm ) sized BSI-CMOS sensor and features BIONZ X processor. On the other hand, Canon 1D MIII has a 10.0MP APS-H (28.7 x 18.7 mm ) sized CMOS sensor .
Sony A9's sensor provides 14MP more than Canon 1D MIII'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.
Another difference between these two cameras is that Sony A9's sensor lacks 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 moire occurring in certain scenes.
Below you can see the A9 and 1D MIII sensor size comparison.
As seen above, Sony A9 has a 1.6x Larger sensor area than Canon 1D MIII. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.
DxOMark Sensor Scores
Both Sony A9 and Canon 1D MIII sensors have been tested by DxoMark. DxoMark scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Of the two cameras that we are comparing, A9 has scored 92, 21 points higher than 1D MIII.