Regarding closed, have you discounted the DT770? Surely the best value proposition although the AKG 371 gets a lot of love around here too.
Honestly, I like the K371 way better ... wich is why I got a pair, great allrounder at 109€, they will be replacing my good old UE 4000 for mobile use.
I don't have direct access a pair of DT 770 Pro, but I know them and have access to both DT990 Pro and Custom Studio, the latter of wich I compared to the K371 just earlier today.
Sound wise, the AKG are superior to the Custom Studio (80 Ohm drivers with base-sliders) in almost every way; more lively, more controlled base, softer treble, just cleaner and more present overall.
On top of that, the DT 770, unlike the Custom Studio, has the overly sharp highs of the 990, something I really can't stand. Now, I don't mind a bright headphone, but sharp highs I can't stand - for older people that might be very different.
Wearing comfort will be very different for people, for me the K371 are comfortable. They are reasonably light, not very large and have a low clamping force. With the foldability and the (very, maybe overly soft) pleather ear pads they are geared more towards mobile use than the DT 770 or Custom Studio. They fit over my ears comfortably, though people with large ears might run into problems.
The K371 are way easier to drive than the 80 or 250 Beyer (lots of head room with all common smartphones), and output impedance of the source has no influence on tonality.
Just my 2 cents.