It's so hard to say, but I'm going to attempt to describe how I see it.
For casual, every day listening, there is a difference, but its not so extreme. I don't want to get into percentages though because I think it doesn't reflect the subjectiveness so accurately.
I honestly believe, if I never ended up in the hobby, the HD600, DT880, would have been more than enough to allow me to feel like I was having the ultimate audio experience.
In critical listening, where I'm glued to the listening experience as if I was going to a concert and giving it my undivided attention, the top tier headphones on my list manage to be much more expressive and life-like. In this instance, they are on two different plains and I have no hesitation in saying that the Orpheus, R10, SR009, HD800, HE-6, LCD-3 is able to do express feelings and nuances in sound (and through that, music) which the mid-tier headphones are not capable.
So, I would say for someone who spends a lot of time listening to music with keen, attentive ears to the audio quality, and for someone who experiences great joy in being as close to realistic sound as possible, the difference is significant. For someone who enjoys music no matter what the audio quality (save for really bad headphones), then the HD600 or DT880 or K701 could be seen as a very respectable mountain top and save a lot of money (and most importantly.... ONE MAY NOT ENJOY THE MUSIC ANY LESS :) It also greatly depends on what you are willing to spend.
Not everyone allows audio quality to affect their music experience (or is sensitive to audio quality). Let's all take a moment of silence to hatefully envy those people (and their wallets) :D
Edited by DavidMahler - 12/3/12 at 11:45am