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