FX v DX .... I have in the majority times found FX images to be better, (less noise) than DX, (D750 v D7200, but certainly D810 v D7200) .........but I think it may depend on the shot and how near you are
say a small bird from 8 to 10 - FX v DX ....... and certainly if you are very near .. at almost cropable portrait head distance .... are less noisy taken from the same distance and cropped FX v DX ........ not sure what the cut off point is
with the latest NR software, especially if you have a clean background, noise can be reduced considerably on the DX image bringing it near the FX ...... in many cases .. but when you have to go into the bird, NR get noticeable
as I said, just my experience
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That's why I don't own DX any more... but it also depends on your uses and how you are comparing them (100% zoom, same size print, 2048x web, etc)
I rely on actual focal length/magnification (expensive) and getting closer. But when that is not an option, the tradeoffs become more vague.
The general tradeoffs as I see them:
FF captures more light per pixel (or area) and therefore has lower noise. But it requires a longer FL which (generally) has a smaller max aperture and therefore may require using a higher ISO.
TC's increase FL for less cropping of the FF (or any) sensor. But they cost 1-2 stops of light and therefore may require a higher ISO. Plus they degrade IQ somewhat and that costs another stop or two in order to regain it (if that's even possible).
DX/cropping doesn't require TC's or longer FL's so you can use a wider aperture/lower ISO, but they have more noise at lower ISO's (same generation/pixel count/smaller pixels).
There is no clear winner here and it will really be dependent on the specific camera characteristics/tradeoffs being compared...
DOF is another quality that varies with FL/TC's/sensor size/cropping...and it's not one that the calculators are much help in with understanding (I can't put it into definitive/empirical terms).
But there is one general truth that can be applied... The larger the size of negative you have (sensor area remaining) the better the image quality will be for any given display/print size.
Sensor resolution doesn't really matter that much because all modern sensors have more than you really need... (ever wonder why DOF/sharpness calculators (COC requirements) don't change with sensor resolution/MP's?)