Sony A7 III has a 24.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz X processor. On the other hand, Nikon D500 has a 21.0MP APS-C (23.5 x 15.7 mm ) sized CMOS sensor and features Expeed 5 processor.
One other difference between these two cameras that is worth mentioning is that Nikon D500'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 A7 III and D500 sensor size comparison.
As seen above, Sony A7 III has a 2.3x Larger sensor area than Nikon D500. 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 A7 III and Nikon D500 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, A7 III has scored 96, 12 points higher than D500.