Both Sony RX100 and Sony RX100 II have 1-inch sized 20.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the RX100 and RX100 II sensor size comparison.
Sensor Size and Resolution Comparison image of Sony RX100 and Sony RX100 II Cameras
Sony RX100 and Sony RX100 II 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 RX100 and Sony RX100 II sensors have been tested by DxO and the results show that RX100 II has a better overall score of 67, 1 points higher compared to RX100's score of 66.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony RX100
66
22.6 bits
12.4 Evs
390 ISO
Sony RX100 II
67
22.5 bits
12.4 Evs
483 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 RX100
or the
Sony RX100 II ,
including hyperfocal distance.