Nikon D500 has a 21.0MP APS-C (23.5 x 15.7 mm ) sized CMOS sensor and features Expeed 5 processor. On the other hand, Sony A77 II has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Bionz X processor.
Another difference between these two cameras is that Nikon D500's sensor lacks 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 D500 and A77 II sensor size comparison.
Nikon D500 and Sony A77 II have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.
DxOMark Sensor Scores
Both Nikon D500 and Sony A77 II 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, D500 has scored 84, 2 points higher than A77 II.