Well, first I’d like to know the higher quality pair you got?
I’m active on r/Headphones (private at the moment) and from my understanding, and experience with higher quality headphones ($1,000+) it has a lot to do with a mixture of tuning and the actual driver itself.
A dynamic driver headphone is pretty simple, it’s a membrane with a magnet and a coil. When the signal moves the membrane, you get sound. Bass notes are from the full movement of the driver and the mids and highs are all in between essentially.
Cheaper headphones use cheaper materials and are tuned not very well. Some headphones show instrument separation very well. Some accurately can reproduce the exact sound the instrument makes (pianos for example)
It has a lot to do with the development and design of the driver and how it’s tuned.
As far as in the head, the effect over ear headphones aims to achieve is what’s called soundstage. That means to be able to reproduce the sound in a 3d field around your head. And some headphones do it much better than others.
Some people prefer a close field where you can seem like you’re on stage with the artist. Some prefer a wide expansive stage like you’re in a concert hall. I prefer more of a middle ground.
Ultimately it depends on the headphone. But
TL;DR, the tuning and design of the driver will determine how much volume you need to get the same result.
Hope that helps, and when r/headphones reopens, there’s a bunch more knowledgable folks that will be glad to help elaborate more.
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