I think the Titanium HD may have a dedicated headphone amp in it, much like the Asus Xonar Essence cards, but I can't confirm that.
A good external headphone amp will certainly give an improvement in sound (e.g. more volume, tighter/deeper bass, more forward and lush midrange and treble, etc), but how big a difference this is, depends on your headphones.
For example, when I went from a X-Fi Xtreme Music to an Essence ST, there was only a slight increase in quality when using my Audio Technica ATH-A900 (40 ohms), which was mainly more transparent/forward midrange and sparkly highs - volume on the X-Fi was already more than enough anyway. The Essence ST wasn't really worth it.
Using my Sennheiser HD650 (300 ohms) though, the difference was huge. Bass was tigher and more impactful, with midrange and treble much more forward and lush. The headphone clearly benefited from amping.
From what I've read, the PC360 can be driven fairly easily from portable source, so pretty much all the X-Fi cards should do well.
Regarding gaming features, I'm not sure how useful any of the X-Fi stuff is these days and their performance benefits are inconsequential. Most games are are slowly dropping support for these features and moving towards software only processing (e.g. BC2 and BF3). Most important features like virtual surround sound are available even on the cheapest cards these days. I don't use any of these features and prefer a clean, unprocessed signal to my headphones, even for games.