Both Sony A77 and Nikon D5500 have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
One other difference between these two cameras that is worth mentioning is that Nikon D5500's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the A77 and D5500 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A77 and Nikon D5500 Cameras
Sony A77 and Nikon D5500 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 A77 and Nikon D5500 sensors have been tested by DxO and the results show that D5500 has a better overall score of 84, 6 points higher compared to A77's score of 78.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Sony A77
78
24.0 bits
13.2 Evs
801 ISO
Nikon D5500
84
24.1 bits
14.0 Evs
1438 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 A77
or the
Nikon D5500 ,
including hyperfocal distance.