FX vs DX

What is the difference, if any, in an image taken with a camera with FX sensor and zoomed in vs. the same image and lens used with a DX sensor camera? In other words is there any advantage to either over the other? I understand the crop factor making lenses used with DX sensors providing more reach, but is this really different than taking an image with FX body and zooming in to the same size final image? Obviously larger pixel count sensors can be zoomed or cropped more.
Also, what about the setting on some cameras to make the FX sensor effectively an DX sensor?
I have currently a D4 and D800 cameras, but considering adding a D500.
Thanks.

The main differences will be in DOF for a given aperture, noise for a given ISO, and dynamic range:

DOF for a given aperture - since on the DX body you are using a wider lens to get the same field of view, for a given aperture you will have more DOF

Noise for a given ISO - assuming the two sensors are made by the same company using the same semiconductor technology, or the same generational node of semiconductor technology, and have the same megapixels (say 24mp) the FX sensor will have better noise characteristics by about 1 stop due to larger pixel sites.

Dynamic range - for similar reasons as above, since each pixel can collect more light, if the same technology generation is employed, you will have about 1 stop more dynamic range headroom.

All that said, if you stay down at base ISO and the resolution of the DX and FX sensor is the same, you will see almost no difference other than the 1 stop or so of dynamic range.  At higher ISOs, the differences become more obvious.

As for setting an FX camera to DX mode, you typically end up with far fewer pixels.  For example your D800 in DX mode is only 15mp while the D500 is 20mp and your D4 is less than 10mp in DX mode.

One of the areas where DX sensors have an advantage is when shooting macro. At the same camera to subject distance the DX sensor provides more DOF and a larger on sensor image (or greater working distance for same size on sensor image). This can be a big advantage when shooting nervous subjects or when its difficult to get close to the subject. However when shooting wide view landscapes in a single capture the FX sensor usually wins hands down with more DR and and the lens being its full width and not cropped by a DX sized sensor.

Accepting the conventional wisdom that a full-frame sensor results in better image quality performance than a cropped sensor and will result in a better capture when cropped to the equivalent size, a question I have is do photographers who have gone from 1.6X, 1.5X, 1.3X, etc. cropped sensors to full-frame have difficulty focusing on the resulting smaller image in the viewfinder of a full-frame sensor, i.e., a songbird's eye?

TonyQ

ajq wrote:Accepting the conventional wisdom that a full-frame sensor results in better image quality performance than a cropped sensor and will result in a better capture when cropped to the equivalent size, a question I have is do photographers who have gone from 1.6X, 1.5X, 1.3X, etc. cropped sensors to full-frame have difficulty focusing on the resulting smaller image in the viewfinder of a full-frame sensor, i.e., a songbird's eye?

TonyQ

Not all cameras are created equal in that regard.  Modern APS-C cameras like the D500 have a large bright viewfinder with a high number of AF points spread across the entire viewfinder which actually makes it easier, not harder to get critical focus anywhere in the frame.