Audeze vs. HIFIMan vs. ??

All I know is I have Quad and Stax. I’ve never heard any A or H that sounded better.

Begs the question, which Hifiman ‘phones have you heard?  Here’s a comparison of the Arya to the Quad planar model by Soundnews.net...

Hifiman Arya ($1600) VS Quad ERA-1 ($800)

I will skip the boring stuff like the build quality and package contents. Arya is double the price of Quads and once you listen to them you will understand why.

Arya is offering at least one or two additional layers of dynamic range; Arya is having more micro-detail information and even an additional layer of sub-bass. In terms of treble performance Arya is completely in another league since it will render even sub-sonic information and has a much better upper-treble performance. There is a drop in the lower treble on the ERA-1 that makes them really easy-going and somehow smooth sounding. ERA-1 will not punish you as much if you are listening to lower-quality material, Arya will show everything be it good or bad.

Arya is also sounding more open, wider, more holographic and really envelops your head, ERA-1 is a bit more up-front sounding.

There is just one single thing that Quad ERA-1 is doing better than Arya and that is the slam. ERA-1 hits harder, on rock and electronica it can be too much at times, it will tire you down in the long run. If Arya would have the same slam and kick it would be the perfect headphone for me.

I haven't owned any Beyerdynamic headphones so can't comment on how Audeze or Hifiman compare to them, and it's not clear exactly what you want to achieve, other than better "sound quality".

I own Audeze LCD-2, LCD-XC, and LCD-4 and Hifiman HE-560.  Audeze have a signature that is a little on the warm side and do bass and mid-range really well, with less emphasis on the highs (which some may find "closed-in" sounding).  The LCD-2 are probably the most neutral, the LCD-XC are the best if you want some bass, and the LCD-4 (out of your budget) are the best, period.  The HE-560 sound very similar to the LCD-2, but a little more neutral.  They do bass well, but are a little more balanced throughout the frequency range.

I would focus more on the type of sound signature you like than the type of driver technology used.  

I would add Focal to your list - the Massdrop Elex is really good for the money, very detailed, comfortable and a more balanced sound.  I haven't heard them, but the Clear is also in your budget.

If you like things really detailed, see if you can find a used pair of Sennheiser HD800.  I think they sound great, but I know they are too "analytical" for some.

Your headphone amp might actually be the weak link.  I had the A2 which is the big brother of the A20.  It had good sound, but was a little under-powered.  There are much better headphone amps available.

I use Audeze LCD-3 when I’m in my home office I use a Dragonfly Cobalt Audioquest dac with my Iphone for listening and does a decent job powering the cans. In my family room I use XLR connections on a Drop Cavalli liquid carbon X headphone amp connected to a SLMS M400 and that works nicely. I also connect the amp to my Bluesound Vault 2i via RCA as well for listening. Both set ups deliver, but I prefer the SMLS for MQA so far. Not a knock on the Bluesound, just my preference. At big_greg is correct on the sound experience.

@big_greg thank you so very much for the comparisons! I hadn't thought of the Focals. I'll take a look.
Happy listening.

Of my open backs I have Beyerdynamic T1, Audeze LCD2, and Hifiman HEX, but my favorite is Sennheiser HD800. I put some Deconi Hybrid earpads on them which improved the sound and increased comfort. They have the best soundstage and do not sound analytical to me.