Both Nikon D500 and Canon 1Ds MIII have 21.0 MP resolution sensors but Nikon D500's sensor is APS-C (23.5 x 15.7 mm ) and Canon 1Ds MIII's sensor is Full frame (36 x 24 mm ).
Since Canon 1Ds MIII's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Nikon D500.
Another difference between these two cameras is that Nikon D500'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 D500 and 1Ds MIII sensor size comparison.
As seen above, Canon 1Ds MIII has a 2.3x Larger sensor area than Nikon D500. 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 Nikon D500 and Canon 1Ds 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, D500 has scored 84, 4 points higher than 1Ds MIII.