HDMI is higher quality.
The first difference is that HDMI technology incorporates content security that is called High Definition Content Protection, also known as HDCP. The other huge difference between Digital Video Interface and High Definition Multimedia Interface is that DVI can only support digital video, and HDMI can support audio and video on the same cable.
This leads to another big difference between HDMI and DVI. The number of cables that need to be used and run during installation. With Digital Video Interface at least two cables are needed. One cable is needed to support the video signal, and one cable or cord is needed to support the audio signal, because DVI can only support video, not audio. With HDMI only one cable is needed for the installation. This is because the HDMI can support all formats of digital video plus it can support multiple channels of audio signal as well.