What is a better cable, HDMI or DVI?

Both HDMI 1.1 and DVI are equal quality as far as video is concerned but only HDMI can carry audio as well. HDMI 1.3 has an option for Deep-Colour support - meaning more colours than maybe some older DVI displays can display. Be aware that all HDMI devices are likely to be HDCP compliant to protect content such as Blu-ray movies while older DVI devices may not have HDCP capability and so will not sure protected images.