I just so happen to have been playing around with switching between the audio output on my geforce gtx 580 (via hdmi), and my X-fi titanium (via 7.1 direct).
I don't think there's anyway to get the x-fi to output hdmi. I've not seen a sound card that outputs hdmi.
As far as quality goes, the x-fi sounds better than the hdmi. It's not cleaner, but the sound card does let me tweak things a little more to my liking. I do think I could get the same effect if I played with my receiver (a harman kardon avr 1600), but it's easier to do on the card.
It's actually very painless to swap between the two in windows 7. All I had to do was go to the control panel, open the sound menu, and set whatever device I wanted to use as "default." I didn't have to uninstall any drivers, remove any hardware, or even reboot.
I was playing around because I wanted to see which sounded better, the video card or the sound card, and also to see if hdmi was a viable replacement for 7.1 direct.
In the end, I stuck with 7.1 direct and the soundcard. In the very best world, either sound cards would have hdmi output, or video cards would allow more tweaking of their sound device.
Another big problem for me is that the video card doesn't have an input jack, so I can't use it with a microphone for games.