Both Panasonic S1 and Panasonic S1H have Full frame sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Another difference between these two cameras is that Panasonic S1's sensor lacks 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 moiré occurring in certain scenes.
Below you can see the S1 and S1H sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic S1 and Panasonic S1H Cameras
Panasonic S1 and Panasonic S1H 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.
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
Panasonic S1
or the
Panasonic S1H ,
including hyperfocal distance.