I always thought back in the day, that the Amiga let you do stuff that didn't look like it was done on a computer. You could do music, graphics, animation, and publishing on the old 8-bit machines - I did a bit of that myself... but for the most part this was just novelty stuff. The Atari user group newsletter I did on the Atari 800 being the one exception.
When the Amiga came out, you could do stuff for it's own sake not just for the sake of doing it with that expensive computer. There was good software aimed at the non-professional users. The EA "Deluxe" stuff, Sonix, Pagestream all were easier to use than their PC counterparts. The multitasking Amiga OS made it easy to use them all at once.
Now, not so much other than bragging rights about being able to do all this way back in 1987 with the same hardware. ;-)