Both Nikon D3200 and Sony A77 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 D3200 and A77 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon D3200 and Sony A77 Cameras
Nikon D3200 and Sony A77 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 Nikon D3200 and Sony A77 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, D3200 has scored 81, 3 points higher than A77.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Nikon D3200
81
24.1 bits
13.2 Evs
1131 ISO
Sony A77
78
24.0 bits
13.2 Evs
801 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
Nikon D3200
or the
Sony A77 ,
including hyperfocal distance.
