Both Sony A65 and Sony A77 II 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 A65 and A77 II sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A65 and Sony A77 II Cameras
Sony A65 and Sony A77 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 A65 and Sony A77 II sensors have been tested by DxO and the results show that A77 II has a better overall score of 82, 8 points higher compared to A65's score of 74.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony A65
74
23.4 bits
12.6 Evs
717 ISO
Sony A77 II
82
24.4 bits
13.4 Evs
1013 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 A65
or the
Sony A77 II ,
including hyperfocal distance.