Computer-monitor connection

Which connection gives me a better image on a full HD flat screen computer monitor:

DVI or HDMI?

HDMI

Thank you Jason for your detailed response. Can you shed some light please. After all, both are digital HD formats. Why do you think HDMI is better, in terms of picture quality?

It must have been early in the morning when I answer your question or computer monitor didn't register. DVI is the answer you wanted. My mistake.