QUOTE (Audible! @ Sep 28 2009, 21:08)

There shouldn't be a difference between the options, but...
What OS?
Will you be gaming much on the machine?
I would check out your software playback options for any "gotchas" with the options you're considering.
Would you buy a different motherboard if you go with the sound card?
Actually there is plenty of difference... I've been battling HDMI on the HTPC for years now, and just now it's getting exciting (maybe "decent" is a better word).
To the OP,
I haven't tested XP, but I'll assume you have Vista or Win 7 (which if you don't, I suggest you move to for HTPC use).
The Gigabyte's HDMI device is not a Realtek device. The 889 is the analog device in that mobo. The HDMI device is an Nvidia 9400. I have used a 9300, which is the same with a slower clock. Nvidia is horrible with their HDMI audio drivers. At first on a 7.1 system, they had the rear surrounds and side surrounds swapped. Then they fixed it, only to swap them again on the latest driver (which by the way you have to dig really deep for... the one on the Nvidia site is usually not the newest). It is a mess. Also, on my 9200m GS laptop, the HDMI device is only 7.1 channel and stereo capable, no 5.1. WASAPI exclusive doesn't work well, not even close.
The Xonar and Auzen are equivalent more or less, but both of them require specific players for bluray bitstreaming of "HD" audio (Dolby TrueHD and DTS HD MA), TotalMedia Theatre and PowerDVD 9 respectively. PowerDVD 9, I have sworn off, there's a lot of bugs, and Cyberlink is not consumer friendly at all, I've used PDVD 7.3, 8 and 9, and with 9, finally I had to return my license because it sucked so much. Starting with 7.3, they started taking out features with every build (update), which in turn you required to play the newer bluray discs. This is one of the many reasons I recommend getting AnyDVD HD for bluray playback. It's the single most useful piece of software in my HTPC.
Arcsoft (Total Media) is more consumer friendly, but their program is also buggy. The fact that you need one specific program for the cards is just wrong in principle anyway. You can still get up to 7.1 LPCM, but with the Xonar (the Auzen is still in the air whether it does this) you can get WASAPI exclusive to work in bypassing the Windows mixer, but it doesn't bypass the Xonar's control panel, where you have to set
manually number of channels and sampling rate. There is no automatic switching, so pretty much negates the practicality of WASAPI exclusive. With the ATI 4000 cards, right now WASAPI exclusive works the best. The Auzen is far more overpriced than the Xonar, which now offers an HDMI-only Slim model. Even the one with the "daughter card", the HDAV deluxe, is less expensive than the Auzen one because the Auzen doesn't come with PowerDVD 9 included (besides being more expensive as well). PowerDVD 9 will cost you another pretty penny, which it's not worth it.
There is no reason to buy any of these though, right now. They're too expensive, and the Nvidia 9400 is an old chip, notwithstanding the bugs. The recent ATI 5800 series and the upcoming rest of the 5000 series have bitstreaming capabilities of HD audio, basically making the Xonar HDAV and Auzen Home Theater HD overpriced if bitstreaming is your goal, and with stuff like WASAPI exclusive it's probable that the 5000 series will work even better than those (like the 4000 series already does). The new CPUs from Intel with GPU incorporated (Clarkdale and Arrandale) will also have an HDMI device with bitstreaming capabilities.
Personally, I am OK right now with an ATI 4670, but I have to jump through some hoops to get non-downsampled audio (which is not a big deal anyway), and have to use a specific build of PowerDVD 8 (2217) which has the least bugs. Newer builds of 8 and 7.3 (which gets parallel updates), and version 9 which came along long after the "usable" builds of 7.3 and 8 came out, suck, especially for HDMI LPCM audio.
Since the 5800 just came out, we're waiting for confirming reports on what its capabilities are. We know it can bitstream with PowerDVD 9, but they haven't said it's only limited to one player, and there's hope that it will allow directshow decoders to bitstream as well. Same with Clarkdale/Arrandale, only those we know work with TMT. It's just getting mainstream right now. I repeat, I would not buy any of those options you mentioned above, they're outdated. The 9400 in age and capabilities, and the Xonar and Auzen in price.