Yes, you have an audio port which have better audio quality than the audio jacks, and that is the S/PDIF optical output (that black square-shaped plug below the black plug). The problem is that you need an amplifier/audio converter which can decode digital signals, as that port can send information in every configuration possible, starting to 2.0 (stereo) all the way to 7.1.
Back to the quality problem: according to mobo's specifications, you should have the VIA VT2021 codec; by looking at the datasheet, all outputs are of the same theoretical quality. Now, the question is if Gigabyte has done some modifications of the outputs; please check the manual from your suppport DVD for detailed specs of the audio.
On the other way, as I was saying in the other post, there is a possibility that you don't have a top-of-the-line amplifier, so you will not hear a difference anyway. When I had the same problem, I was able to tell the difference solely because of a good amplifier (Cambridge Audio) and a pair of decent speakers (full range home-made). On my PC speaker system (Altec Lansing), I was not able to tell the difference in quality between front/rear/sides/C+S outputs...