DVI also has HDCP so that difference is not a difference at all. Older DVI products DID lack it, but all new(even back in 2007 and earlier) stuff has it.
HDMI was released and based entirely on the DVI single link connection(good enough for 1080p video). They simply made a smaller connector and added digital audio into the mix.
Future versions of HDMI have added extras like network as well. HDMI should still be backward compatible with DVI(but without audio)
For picture quality, they will look exactly the same on you monitor or TV. And with Display Port getting popularity(no fees), HDMI may be replaced soon anyway.
http://en.wikipedia.org/wiki/HDMI