Both Olympus E-M5 III and Olympus E-M1 II have Four Thirds sized 20.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
One other difference between these two cameras that is worth mentioning is that Olympus E-M1 II's sensor doesn't have an 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 E-M5 Mark III and E-M1 II sensor size comparison.
Olympus E-M5 III and Olympus E-M1 II have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.