Panasonic BGH1 has a
10.2MP Four Thirds (19 x 13mm ) sized MOS sensor . On the other hand, Panasonic GH5S has a
10.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine 10 processor.
One other difference between these two cameras that is worth mentioning is that Panasonic GH5S'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 BGH1 and GH5S sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic BGH1 and Panasonic GH5S Cameras
Panasonic BGH1 and Panasonic GH5S 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 BGH1
or the
Panasonic GH5S ,
including hyperfocal distance.