Panasonic S1 II has a
24.0MP Full frame (35.6 x 23.8 mm ) sized Partially-Stacked CMOS sensor and features Venus Engine processor. On the other hand, Panasonic BS1H has a
24.2MP Full frame (35.6 x 23.8mm ) sized CMOS sensor .
Another difference between these two cameras is that Panasonic S1 II'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 II and BS1H sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic S1 II and Panasonic BS1H Cameras
Panasonic S1 II and Panasonic BS1H have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the 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 II
or the
Panasonic BS1H ,
including hyperfocal distance.