Both Sony A99 and Nikon D5500 have 24.0 MP resolution sensors but Sony A99's sensor is Full frame (35.8 x 23.8 mm ) and Nikon D5500's sensor is APS-C (23.5 x 15.6 mm ).
Since Sony A99's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Nikon D5500.
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 moire occurring in certain scenes.
Below you can see the A99 and D5500 sensor size comparison.
As seen above, Sony A99 has a 2.3x Larger sensor area than Nikon D5500. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.
DxOMark Sensor Scores
Both Sony A99 and Nikon D5500 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, A99 has scored 89, 5 points higher than D5500.