I've got a pair of grado 325i's I run through a Beyerdynamic headphone amp - from a half decent source and I can hear those differences just fine!You won't, not on a set of cans or a home hifi system - it notices as soon as you start putting the sound through a speaker with a greater sound range - like the difference between your phone speaker and you hifi but on a grander scale.
As a dj I can stand there and tell if another dj is using illegal downloads - when they're only listening to it through the monitor speaker they don't think it notices but through the main system it really really does!!!
Ps as a dj there's only one set I'd recommend and they ain't in ear ones... Sennheiser hd 25-1 mkII
Best in ears I ever had were the ultimate ears triple fi. 10 - they were uncomfy and useless for running but the sound was amazing, even compared the some shures I had that cost twice the price.
I was going to recommend those but amazon says they're discontinued. Really annoying as I lost my pair a few years ago and never replaced them, guess I won't now!