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