Both Sony A68 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 A68 and A77 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A68 and Sony A77 Cameras
Sony A68 and Sony A77 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
Both Sony A68 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, A68 has scored 79, 1 points higher than A77.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony A68
79
24.1 bits
13.5 Evs
701 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
Sony A68
or the
Sony A77 ,
including hyperfocal distance.