Just for you Dave
It is a common misunderstanding that sharpness is defined by the number of pixels. That has an impact of course, but it's relatively minor compared to the size/area/format of the sensor - size matters, and bigger is better. It's physics (as opposed to marketing talk

) and the bottom line is basically this - using the same lens at same settings, on average images will be about 10-12% sharper on full-frame.
What we call 'sharpness' has two components - resolution (the fineness of detail) and contrast (how clearly those details are shown). Of the two, contrast has the most influence on our visual perception of sharpness. The physics of it is, as resolution demands go up, so image contrast goes down. It's like a car that will accelerate from 0-60 in six seconds, takes twice that time (or more) to get from 60-120. The more you ask, the harder it gets, and lenses are the same. DX cameras have smaller sensors, so they demand higher lens resolution - 1.5x higher for DX vs FX.
Good explanation here, but just look at the first couple of diagrams that show as the black and white lines get closer, so the contrast gets lower. Blacks get lighter, whites get darker, ultimately turning to grey porridge
http://www.cambridgeincolour.com/tutorials/lens-quality-mtf-resolution.htm
Lens MTF tests (Modulation Transfer Function) compare resolution vs contrast. Here's one example of MTF graphs for four 84mm f/1.4 lenses, plotting contrast at different resolution levels - 10-lines-per-mm, 20, 30, 40, 50
https://www.lensrentals.com/blog/2016/04/sony-fe-85mm-f1-4-g-master-lens-mtf-and-variance/ Just look at the Y-axis up the left (which is the centre of the frame, you can ignore everything else*) and note how with every increase in resolution of 10-lpmm, contrast drops by roughly 0.1 (that's actually 10%, with 1.0 at the top being 100% theoretical maximum). The orange 20-lpmm and green 30-lpmm lines are good ones to look at. That's a decent standard for high quality working, and conveniently, the difference between them is 1.5x - exactly the Nikon DX crop factor. In other words, if you put the same lens on a DX camera with 20mp sensor, the green line shows the standard of sharpness; but on a 20mp FX camera, you'll get the orange line and a jump of maybe 10-12% in sharpness.
*Those graphs are only a snapshot of lens performance. In particular, they're at f/1.4 only, with % contrast up the left, and mm from the centre of the frame along the bottom. It's worth noting the Zeiss Otus 85/1.4 with outstanding sharpness in the centre at f/1.4, though the others catch up and get much closer at f/2.8-4. That's what you get for £4k