DVI = Carries video only
HDMI = Carries video and audio
If the same quality components are used for the DVI and HDMI ports, then there should be no video quality difference.
HDMI can send audio signals to the monitor assuming you install the audio driver for AMD video cards or connect a pass-thru cable from the sound card to the nVidia card. If the monitor does not have speakers, then there no real point to use HDMI.