Both Canon 6D and Canon 1D X III have Full frame sized 20.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the 6D and 1D X MIII sensor size comparison.
Sensor Size and Resolution Comparison image of Canon 6D and Canon 1D X III Cameras
Canon 6D and Canon 1D X III 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 6D and Canon 1D X III sensors have been tested by DxO and the results show that 1D X MIII has a better overall score of 91, 9 points higher compared to 6D's score of 82.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Canon 6D
82
23.8 bits
12.1 Evs
2340 ISO
Canon 1D X III
91
24.2 bits
14.5 Evs
3248 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 6D
or the
Canon 1D X III ,
including hyperfocal distance.