List your state of art headphones for smart phone use!

I am looking for over the ear headphones that can play at a satisfactory volume and do not drain the battery.
I currently have Sony Pro MDR 7520 headphones that list at $500 and are on Amazon for $275.
They are comfortable and fairly good for the price.
I use an Audioquest dragonfly cobalt D/A with my iPhone, iPad, and laptop.
If I moved up to $1000 or more what would be much better?
Are earbuds an alternative at all?
At home I use Stax L700 and get very close to SOTA sound quality with a Stax tube/fet driver amp.
I do not expect the same Stax sound quality.
Can I get close to my home headphone quality?