Nikon Z 6 has a 25.0MP Full frame (35.9 x 23.9 mm ) sized BSI-CMOS sensor and features Expeed 6 processor. On the other hand, Panasonic S1 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 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 Z 6 and S1 sensor size comparison.
Nikon Z 6 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.