Both FujiFilm AV200 and Panasonic ZS20 have 1/2.3-inch sized 14.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the AV200 and ZS20 sensor size comparison.
Sensor Size and Resolution Comparison image of FujiFilm AV200 and Panasonic ZS20 Cameras
FujiFilm AV200 and Panasonic ZS20 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
FujiFilm AV200
or the
Panasonic ZS20 ,
including hyperfocal distance.