Canon 6D has a 20.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Digic 5+ processor. On the other hand, Canon 1D MIII has a 10.0MP APS-H (28.7 x 18.7 mm ) sized CMOS sensor .
Canon 6D's sensor provides 10MP 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.
Below you can see the 6D and 1D MIII sensor size comparison.
As seen above, Canon 6D 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 Canon 6D 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, 6D has scored 82, 11 points higher than 1D MIII.