The STX actually does better with high impedances, because of its output impedance. It can do 7 Vrms into high impedance loads, more than enough to drive anything short of an AKG K1000 to 110 dB (and maybe Hifiman HE-6 depending on if the manufacturer specs are wrong).
"much better quality amp" is debatable too. The STX has very good distortion and noise, better than a lot of the crap that's sold for mega bucks. There are better alternatives for low impedance headphones, but probably nothing will be audibly different at high impedances unless the other amp is intentionally colored.
As for the doubt that a sound card can drive big headphones, the STX uses a similar amp section to the Fiio E9 (though I believe it's better with distortion, but can't be sure). 7 Vrms is the same voltage output as the Schiid Asgard, and manufacturer specs there say <0.1% THD at 1 V which is pretty unimpressive for solid-state. The Essence STX meanwhile is claimed to have 0.003%, but that's not likely to always pan out in the real world (neither is the Asgard's 0.1%!)
Edited by Head Injury - 12/15/11 at 4:37pm