Actually, the Magni is rated Frequency Response: 20Hz-20Khz, -0.1db, 2Hz-200KHz, -3dB.
The STX is rated Frequency Response (-3dB, 16bit/44.1KHz input) :
10 Hz to 90 KHz
So the Magni might be "truer" from 20hz-20Khz given the lower -0.1db compared to the STX's rating of -3db for it's frequency range, and when rated at -3db, the Magni has the wider frequency response.
I used to own the STX sound card, but I now own the Schiit Asgard 2 and use an ODAC. I have owned a few other amps, including the Objective 2 amp which is often cited as comparable to the Magni. I also own a Xonar DX in another computer. Everything I have read indicates that the Magni has the better headphone amp, and I have no reason to doubt that based on my experience, whereas as the DAC in the STX is a small step up over the DAC in the Xonar D1/DX series (which you might not even notice much).
My advice is this:
If the DT770s are your first good set of headphones and this is your first DAC/headphone amp purchase over basic computer audio, it's gonna sound really good. Plus, the STX has an extra hookups for speakers should you want to add a desktop multimedia setup later on.
On the other hand, if you see this as the first step into the headphone audiophile hobby and could see wanting to upgrade in a couple of years, the advantage of the DX/D1 with the Magni is that you can eventually add a better quality external DAC with optical input as an upgrade and still use the DX/D1 Dolby Surround. You could do this with the STX as well, but then you would need an external headphone amp, too.
As for which could sound better to you? Impossible to say. However, the Magni WILL definitely drive low impedance headphones better (32 ohms or less) should you buy more headphones (a plus if you are getting into this hobby), AND it will definitely drive the DT770 250 ohms louder than the STX, probably louder than you should listen to them if you enjoy your hearing