Both Canon 1Ds MIII and Nikon D6 have 21.0 MP resolution sensors but Canon 1Ds MIII's sensor is Full frame (36 x 24 mm ) and Nikon D6's sensor is Full frame (35.9 x 23.9 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 D6.
Below you can see the 1Ds MIII and D6 sensor size comparison.
Canon 1Ds MIII and Nikon D6 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.