Both Sony A6300 and Nikon D5600 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 D5600'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 A6300 and D5600 sensor size comparison.
Sony A6300 and Nikon D5600 have 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 A6300 and Nikon D5600 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, A6300 has scored 85, 1 points higher than D5600.