BOTH DVI and HDMI are "Digital" video connection standards
The advantage of HDMI is that in addition to the video signal it can also carry audio and remote control signals.
... not that either of those things are particular advantages on computer monitors.
Even on a computer monitor that has built in speakers those speakers generally suck.
My "newish" HDMI monitor has built in speakers.
How do they sound? I frankly have no idea, because while my monitor is HDMI, neither my computer or video card has an HDMI jack, so I'm connected with an HDMI-to-DVI cable.
No need for the built in speakers anyway as it probably wouldn't add anything to my 275watt 7.1 Altec-Lansing sound system, so I simply never bothered connecting them