Both Sony A55 and Sony A37 have APS-C sized 16.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the A55 and A37 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A55 and Sony A37 Cameras
Sony A55 and Sony A37 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 A55 and Sony A37 sensors have been tested by DxO and the results show that A37 has a better overall score of 75, 2 points higher compared to A55's score of 73.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony A55
73
23.0 bits
12.4 Evs
816 ISO
Sony A37
75
23.3 bits
12.9 Evs
799 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 A55
or the
Sony A37 ,
including hyperfocal distance.