I own the Stax Omega. They are amazing phones, but they can also be very very demanding as far as upstream components are concerned. I have really heard them at their best in someone else's system, specifically, a system with an Audionote M-8 linestage and DAC-5 signature digital source and Verdier/Allaert phono setup. In my own system, I am a bit bothered by the dry sound of my solid-state stuff (Levinson Ref. No. 32 and Naim CDS3). For detail, speed and complete freedom from resonant overhang, the Stax are hard to beat.
I have not heard the Qualia phones, but I am sure they are very good. I really liked the dynamic phones Sony use to make about five years ago that cost about $500. I expect that a $3,000 version of a Sony would be an improvement.