Both Sony A77 II and Nikon D3200 have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the A77 II and D3200 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A77 II and Nikon D3200 Cameras
Sony A77 II and Nikon D3200 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
Both Sony A77 II and Nikon D3200 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, A77 II has scored 82, 1 points higher than D3200.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony A77 II
82
24.4 bits
13.4 Evs
1013 ISO
Nikon D3200
81
24.1 bits
13.2 Evs
1131 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 A77 II
or the
Nikon D3200 ,
including hyperfocal distance.