Both Nikon D5100 and Sony A580 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 D5100 and A580 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon D5100 and Sony A580 Cameras
Nikon D5100 and Sony A580 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
At Camera Decision, we also look at Dxo Mark sensors when available as we think it is a good indicator of image quality.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Nikon D5100
80
23.5 bits
13.6 Evs
1183 ISO
Sony A580
80
23.8 bits
13.3 Evs
1121 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 D5100
or the
Sony A580 ,
including hyperfocal distance.