If you've got an Essence STX and aren't looking to drive certain multi-balanced armature IEMs, you can probably focus more on trying different headphones rather than source gear. It's just a suggestion, but I'd consider venturing outside of the Audio-Technica lines, since many other companies produce good headphones as well. If you want to step up, there's a lot more room for improvement with headphones and new music rather than other parts of the signal chain. Well I guess you can explore vacuum tube-based amps if you really want and prefer to experiment with sounds*** by buying new hardware rather than software controls, but particularly the cheaper OTL types would generally be poor matches with Audio Technicas because of the impedance.
***that's experimenting with sounds by degrading them in some sense, arguably in a way that makes them sound better. It depends on your preferences, but at least in a traditional sense of fidelity, you would have to call that lower fidelity rather than Hi Fi.
Here's a review of the Essence STX. As you can see in the notes, there may be some YMMV as well as YCMV (your computer may vary):
http://www.stereophile.com/content/asus-xonar-essence-ststx-soundcards-measurements
Those kinds of figures above are better than a lot of more expensive gear, by the way, and generally they're quite beyond the capability of human hearing to distinguish. This may not always the be case with some headphones where there are significant interactions because of the STX output impedance.
Particularly if you're new to high-end audio, be sure to take any kind of reviews and advice--and I say anybody's, including mine--with a huge grain of salt, for a variety of reasons. Gear comparisons are rarely done in a systematic fashion and with any proper experimental controls. Small changes in volume can make for big differences in perception, and people rarely match the volume between two devices or listening sessions when doing comparisons. Expectation bias is king; people often just hear what they want to hear. Often times, huge differences that people claim to hear tend to disappear when people don't know what they're listening to.
Edited by mikeaj - 2/10/12 at 9:07pm