Windows 7: ATI Radeon AMD HD 6670 2GB Won't Go Past 1920x1080 Resolution

HDMI, if your monitor has built in audio/speakers and you wish to view DRM protected media using your graphics card's built in support, otherwise just use DVI for resolution flexibility during gaming..

HDMI,works better and looks more clear when i connect my computer to the living room tv on 1080p and the audio is in the same connection so that's a big plus.

Dvi and hdmi are the same, just hdmi carries audio, if you need it.
Hdcp has been included on pretty much every monitor made in the last 4 or so years.

I have an older Samsung 19" LCD that doesn't have hdcp and won't play a bluray using the dvi port, but does play using VGA. I use this monitor when I build computers and found out it doesn't have hdcp last week when I put a bd rw in a friends machine and was testing it with a bluray movie.

Does HDMI 1.4a support resolutions like 2560x1600p though? I've always thought you needed either Dual Link DVI or Displayport to achieve those resolutions...

I believe they are upping the specs for hdmi resolutions, but not sure if they are in effect yet.
I should have said that Current hdmi and dvi are the same at 1200p and lower.
The video signals in both cables are the same. You can use a straight dvi to hdmi cable if you didn't have hdmi on your video card.
Some video cards had audio support on one of the dvi ports, my old ati3650 had audio included on the yellow dvi port, white dvi port was only video.

Oh, I just remembered that our HD Editor is using an ati 3870 and we are using a pair of dvi to hdmi cables since the 24" 1920x1200 monitors only have VGA and hdmi ports.