From my experiences, the Realtek sounds a bit more flat, with less bass. The Xonar DG has a better punch, possibly better mids, and more sparkly highs, though I am unsure if the sibilance is more or the same as the Realtek. This was an upgrade from the ALC892 to the Xonar DG. Most people will respond with the Xonar DG being better in here, other tech websites, and other audiophile websites like Head-Fi. If you were using more analytical headphones with more clarity, then you may find a significant difference, otherwise, it's not devastatingly different to the point where you will say that the Xonar DG is 1000% better than the Realtek. If your onboard was a little bit older, Sigmatel 9227 for example, there should be a considerable difference.
Specs-wise, the Xonar DG should theoretically amp your headphones better if your headphones ever need it, though the on-board can produce louder volume from Windows Audio settings.