Both Sony A7 II 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 II and RX1 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A7 II and Sony RX1 Cameras
Sony A7 II and Sony RX1 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.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It 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. Sony A7 II and Sony RX1 sensors have been tested by DxO and the results show that RX1 has a better overall score of 93, 3 points higher compared to A7 II's score of 90.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony A7 II
90
24.9 bits
13.6 Evs
2449 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 II
or the
Sony RX1 ,
including hyperfocal distance.