Both Sony A7 II and Sony RX1R have Full frame sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
One other difference between these two cameras that is worth mentioning is that Sony RX1R'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 A7 II and RX1R sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A7 II and Sony RX1R Cameras
Sony A7 II and Sony RX1R 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
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 RX1R sensors have been tested by DxO and the results show that RX1R has a better overall score of 91, 1 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 RX1R
91
25.0 bits
13.6 Evs
2537 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 RX1R ,
including hyperfocal distance.