HDMI is basically DVI video w/ audio through in the same cable but difference connector. That is why you can have a simple little DVI to HMDI adapter. The only advantage of HMDI onboard would be for Home Theater PC's or if your monitor has an HDMI connector and you dont want to worry about getting an adapter or DVI --> HMDI cable. Watch out for some cards as only certain ones actually carry audio through the HDMI port.
I've actually hear of people having issues with their HMDI video, especially with VISTA 64bit. My buddy can not get his to work, something to do with media rights protection or something.
I like to stick with DVI unless you have a compelling reason to do otherwise. I have a DVI --> HMDI cable so I can hook my PC to my LCD tv when im feeling frisky but I still have to unplug and replug to get it working.
Lamens terms. There is no quality difference in video between HMDI and DVI