Sensor size
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Sensor size

The largest difference - no pun intended - between the Nikon D750 and the D500 is in terms of sensor size. There's a small disparity in resolution (the D750 offers 24MP whereas the D500 lags a little, at 21MP) but more significant is the fact that the D750's sensor is full-frame. The D500, by contrast, is built around a smaller, DX format (APS-C) sensor, which introduces a 1.5X crop factor, meaning that a 50mm lens on the D500 offers a field of view equivalent to a 75mm lens on the D750. There is a plus side to shooting on a DX-format camera though - the 1.5X increase in effective focal length is very handy for telephoto shooting. 

Leaving aside the effect of the crop factor, typically, we'd expect full-frame sensors to offer better image quality in poor light, at high ISO sensitivity settings, and broader dynamic range, compared to APS-C and smaller sensors. The D500's sensor is very good, but physics is physics, and at any given ISO sensitivity, the D750's noise performance is about one stop better than the D500.

In terms of dynamic range, the D750 offers around 0.8EV more dynamic range at base ISO than the D500, which might not seem like a lot, but it's enough to make a difference in some shooting scenarios (like the scene above, which was exposed in Raw mode for highlights, with shadows and mid-tones brightened in post). On the flip side, the D500 provides an electronic first curtain shutter option, which allows landscape photographers to ensure vibration-free images – something that can be a challenge with the D750. 

Verdict: Both cameras offer excellent image quality, but if you need the extra dynamic range, the D750 is the better camera.