And THAT is the other crucial thing to understand, in my opinion; this difference is "simulated"; it's a perception created when doing a specific comparison.
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Yeah, I fear we don't always distinguish between analog and digital resolution. The lens creates the analog image, which the digital pixels merely try to reproduce it well.
Sports and wildlife people favor DX because it APPEARS TO magnify the view from the lens they have, by about 1.5x. Which is good, certainly can be "good enough", but it is not the same as actually using the longer lens on FX (depending on the quality of the two lenses, but FX is the way to bet, if you can afford the lenses). The sports photogs seen at the Olympic or NFL sidelines are not using DX cameras (today).
The lens has a resolution parameter, sometimes called line pairs per mm, or line pairs per screen height, etc.. But the lens image definitely does have a resolution (shows a certain amount of detail), which digital pixel sampling merely tries to reproduce the best it can. The digital pixels can never improve the lens image, actually can never quite fully reproduce the analog resolution, but can copy much of it.
Enlargement (magnification) directly reduces this original lens resolution, proportionately. Twice as large is half as sharp, numerically. We know that a printed 6x4 print looks sharper than an 8x10, which in turn looks sharper than wall mural size. Enlargement reduces resolution, and DX requires half again more enlargement than FX.
Cropping the image in the DX camera, or in the photo editor later (to same cropped size), reduces the lens image resolution the same amount (the subsequent enlargement does this).
However, DX sensor cropping retains all of the sensor pixels.. say 24 megapixels on the DX sensor.
Which in turn is reproduced better (by digital pixel sampling resolution) than if we cropped the FX 24 megapixels in the photo editor later, to be only say 10 megapixels remaining then.
24 megapixels shows the cropped and enlarged lens image better than 10 megapixels can. But neither can improve the reduced original lens image.
So... make no mistake, these pixels are only greater digital pixel sampling resolution to better reproduce the lesser cropped lens image resolution (due to the greater enlargement necessary).
But again, 1.5x is not a huge factor.