Here is what happens when I run my FF vs APSC at the same framing at the same aperture (because I am aperture-limited with my zoom) at high ISO.
First you can see the differences in DOF, and with portraiture, that can be important. Not so much with product shots...
Also, you can see the differences in ISO and detail rendering. Two of Canon's most recent APS-C and FF offerings, shows the differences.
These differences can mean a difference in an okay deliverable to a client vs a very nice attention-grabbing result depending on the content in the image around the subject, plus how you crop, post process, and use the results. Are these differences noticeable as a web print or even a magazine print (which doesn't mean high quality or high resolution)? Most of the time.... most likely no. These images below are resolutions of a 5x7, maybe, and they are noticeable to me at that size. Also some of us want to make sure we use the best tools we can reasonably apply to what we shoot. That is the same no matter what topic you discuss. Tools, cars, appliances, restaurants, etc. you name it, and these same discussions occur. 
People that discuss this and get all up in everyone's faces about the lack of differences seem, to me anyways, like those that go to the street scene and discuss how their turbo'd 4 cylinder is only about .6 second behind somebody else's V8 in the quarter mile. They don't understand that a) that is well over 6 car lengths and is huge in a race and b) it takes ever-increasingly amounts of money to drop just tenths in the quarter mile, the closer to 10 sec you get.
There are those that say "bah, he is only about .5 second behind that guy there", and others that will just roll their eyes because they have experience with how large a difference that really is.
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