Both Sony HX50V and Sony RX100 III have 20.0 MP resolution sensors but Sony HX50V's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Sony RX100 III's sensor is 1″ (13.2 x 8.8 mm ).
Since Sony RX100 III's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Sony HX50V.
Below you can see the HX50V and RX100 III sensor size comparison.
Sensor Size and Resolution Comparison image of Sony HX50V and Sony RX100 III Cameras
As seen above, Sony RX100 III has a 4.1x Larger sensor area than Sony HX50V. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in 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 HX50V
or the
Sony RX100 III ,
including hyperfocal distance.
One thing to watch when comparing these two: they have different sensor sizes
(1/2.3-inch versus 1″ ),
so compare them at the same framing rather than the same focal length.
Put the same focal length on the smaller sensor and it will show less depth of
field, not more, because it also crops tighter. The calculator shows the
full frame equivalent focal length for each body so you can match the framing.