Both Sony A7 II and Panasonic S1 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 moire occurring in certain scenes.
Below you can see the A7 II and S1 sensor size comparison.
Sony A7 II and Panasonic S1 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.