Panasonic S1H has a
24.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Venus Engine processor. On the other hand, Sony A9 III has a
24.6MP Full frame (35.6 x 23.8 mm ) sized Global Shutter sensor and features BIONZ XR processor.
One other difference between these two cameras that is worth mentioning is that Sony A9 III'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 S1H and A9 Mark III sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic S1H and Sony A9 III Cameras
Panasonic S1H and Sony A9 III 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 S1H
or the
Sony A9 III ,
including hyperfocal distance.