Both Canon G7 X and Sony RX100 III have 1" sized 20.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the G7 X and RX100 III sensor size comparison.
Canon G7 X and Sony RX100 III have 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 Canon G7 X and Sony RX100 III 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, G7 X has scored 71, 4 points higher than RX100 III.