Both Canon 5D MII and Canon 1Ds MIII have Full frame sized 21.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the 5D MII and 1Ds MIII sensor size comparison.
Sensor Size and Resolution Comparison image of Canon 5D MII and Canon 1Ds MIII Cameras
Canon 5D MII and Canon 1Ds MIII have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It 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. Canon 5D MII and Canon 1Ds MIII sensors have been tested by DxO and the results show that 1Ds MIII has a better overall score of 80, 1 points higher compared to 5D MII's score of 79.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Canon 5D MII
79
23.7 bits
11.9 Evs
1815 ISO
Canon 1Ds MIII
80
24.0 bits
12.0 Evs
1663 ISO
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Canon 5D MII
or the
Canon 1Ds MIII ,
including hyperfocal distance.