If you have the proper gear (which will usually cost you at least as much as the headphones themselves due to the way hi-fi market works) then you might say the difference between let's say Beyerdynamic T1's and DT880's is big enough to justify the price gap. I have both of these (plus all other "usual suspects" in the mid-end like the HD650, DT990, K701, etc.) so I can speak from personal experience.
In other words, if you have a high end headamp and a high end source like a really good DAC or CD player, and you're listening to material that is complex enough, and at the same time well recorded and mastered enough, then going from DT880's to T1's will be a noticeable jump, not a huge difference, it's not going to revolutionize the way you listen to music and suddenly make everything sound magically good, but it will be enough of a difference to easily notice which headphone is clearly the superior one.
You will notice the bass is just that bit more extended, just that bit more tight, the punch of the bass is somehow more separated from the rest of the sound, the mids have that small bit more fullness and texture, a bit more realism and naturalness, highs are a bit more sparkly and fast sounding like they have a higher resolution, and details pop out at you more clearly, overall sounds seems a bit smoother and effortless, the soundstage feels a bit bigger and everything sounds closer to being at the spot where the music was recorded. In other words, a lot of small improvements all across the board, really tiny improvements sometimes, but when you put them all together, it makes listening to the music feel more natural and realistic, and therefore more pleasant. So yea, if you have the gear, then it's worth it.
However, if you have inferior gear that can't cope with the quality levels of the high end headphones, you might end up with an opposite effect, and actually get a worse sound experience out of expensive headphones than you would out of cheaper ones.
The most important benefit of T1's over DT880's (or high end over mid end headphones in general in my experience) is the smoothness and the effortless feel. It's something I really can't describe in words and has to be heard in order to get it, but music seems to flow out the T1's more effortlessly, which really makes them feel overall a bit clearer and at the same time more easy to listen to, it almost totally eliminates listening fatigue. This is a huge over-exaggeration, but it's like slowly pouring sand out of a bottle compared to pouring water out of a bottle. You can pour them both out at the same rate, really slowly, but the water will flow out more nicely and smoothly.
The thing that's most disappointing when going from mid end to high end headphones is the actual sound stage, imagining and that projection of sound that would make you feel like you're listening to high end speakers or a live performance in front of you. This is something that no headphone does very well in my experience. Even the HD800 which is known for sound stage and imaging doesn't compare to a decent pair of bookshelf speakers (considerably cheaper than the headphones) in a half decently acoustically treated room. Not even with amps like the SPL Phonitor which have really advanced crossfeed circuits that should simulate that.
My problem, and I'm sure a lot of other people with high end setups feel the same, is that once you reach a certain level of quality as far as the equipment goes, it starts to get really hard to find music material that justifies using that setup over a much cheaper one, because it just wont sound "better enough". You begin to realize that 70% of music on the market is really badly recorded and mastered, especially the new stuff, and it's simply not worth "wasting" your expensive headphone on it. So it gets difficult to find material that you like both for it's musical quality and recording quality.