Panasonic BS1H has a
24.2MP Full frame (35.6 x 23.8mm ) sized CMOS sensor . On the other hand, Panasonic S5 II X has a
24.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Venus Engine processor.
One other difference between these two cameras that is worth mentioning is that Panasonic S5 II X'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 moiré occurring in certain scenes.
Below you can see the BS1H and S5 Mark II X sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic BS1H and Panasonic S5 II X Cameras
Panasonic BS1H and Panasonic S5 II X 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 BS1H
or the
Panasonic S5 II X ,
including hyperfocal distance.