Both Sony A7 III and Sony RX1 have Full frame sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the A7 III and RX1 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A7 III and Sony RX1 Cameras
Sony A7 III and Sony RX1 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.
DxOMark Sensor Scores
Both Sony A7 III and Sony RX1 sensors have been tested by DxoMark. DxoMark scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Of the two cameras that we are comparing, A7 III has scored 96, 3 points higher than RX1.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony A7 III
96
25.0 bits
14.7 Evs
3730 ISO
Sony RX1
93
25.1 bits
14.3 Evs
2534 ISO
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 A7 III
or the
Sony RX1 ,
including hyperfocal distance.