my 2 cents..
I had the 7506 for many years and now HD280 . They work for Microphone tracking stuff to prevent leakage and feedback squeels for tracking.
For mixing they are not used and total hobby opinion, they kind of suck compared to openbacks for mixing.
Openbacks I compared the Beyer 880 and Takstar 671 ($60 openbacks) and the open backs are really a wow tool for that listening mix thing because the bass isnt all exaggerated as with the closed backs. Just try it and see for yourself.
then like most headphone gearheads the path leads to audiophile stuff and ohms and amps.
32,54,250,600 etc... this includes the headphone amp obviously, if going down that hole of technology and terms.
as for headphone amps, I think its like everything else. can you hear the upgrade? etc..
I got a original rev 1 Grace Design, a lot of over engineering for the pro's and interesting story of Bob Ludwig and the Grace team.
of course this cost is a lot to me and nothing to someone with that kind of cash.
in comparing numerous headphone amps on interfaces and such, my Line 6 UX8 happened to have a well designed amp section and they recommend 250ohm and it was the flagship higher end unit to compete with ProTools, professional use that didnt materialize for the UX8....anyway its within 90% of the Grace imo. But both of these are better than the UX2 headphone interface amp and many others I tried.(which are all made for 32ohm for the most part- generic standard design).
The biggest difference in the better amp was handling the bass which Garrw mentioned and was true, the main difference in the extra horsepower of an amp seems to be the low end as they all seemed to do high freqs and mids well. Im not sure why...but they do have a bass with more clarity.
None of the amps sound horrific, the 32 ohm sound fine and all that too, but comparing there is some small % of difference. YMMV...
Then reading the articles on mixing with headphones debates, headphone mixing has its few success stories, and the other thing is the "crossfeed" .
The ears hear both speakers in a car and with active studio monitors in a room so theres a cross-mono-mix thing both ears hear both speakers and so headphones can ruin that.
So the crossfeed button on a headphone amp is great for a HR recording, or adding the crossfeed plugin on the DAW master buss is a very noticeable simulation to mimic your monitor-room soundfield which is kind of a stereo / mono mix soundfield.