Both Sigma SD1 and Sigma SD1 Merrill have APS-C sized 15.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Another similarity between these two cameras is that both Sigma SD1 Merrill and Sigma SD1 sensors lack anti-alias (Low-Pass) filters. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the SD1 and SD1 Merrill sensor size comparison.
Sigma SD1 and Sigma SD1 Merrill 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.