I think for image quality they are pretty much comparable... the advantage of HDMI is that it can carry an audio signal as well a video signal, where as DVI is just video only. So if you have speakers or something built into your monitor and don't want to mess around with additional cables you should use HDMI, other than that though it shouldn't matter.
But if your monitor has both ports you can use both at the same time if you need to, theres usually just a button on the monitor to switch inbetween inputs.
I just installed a PB278Q with an Asus GTX 660 TI and initially hooked it up with HDMI. I was only able to get to a lower than native resolution with the HDMI cable, maybe 1600x900 (I don't remember for sure). It would not support native resolution. I added the DVI cable and was able to immediately set it to 2560x1440. The display quick start paper was a bit misleading on that.
It's a gorgeous display. For years I used a 21" Sony Triniton (actually 19.8" diagonal) and it finally started heading south. So I was torn between the $1000 Samsung 27" (I forget the model number--the 990?) and this one; I have a bunch of Samsung around the house and am satisfied with those products. Considering the high Samsung quality, I could hardly be more satisfied than I am with this Asus. I have almost two times the real estate on this Asus (2560x1440 vs. 1600x1200) as on the old Sony and, while the Sony display was great for glass, this is so much sharper, and about twice as bright (subjective assessment).
The only thing I don't like, and this is a standard problem with WinXP (don't know about Vista or Win 7 or that abominable follow-on to Win 7) is that the dot pitch is so tight (108dpi) that I have to use custom fonts at 113% to get an inch to an inch, and Win XP sometimes renders these fonts outside of where they should be in dialog boxes. I could run it standard at 96dpi, but everything would be slightly too small.
I don't do gaming, only CAD, PhotoShop, Office, and a bunch of other stuff. CAD makes good use of the high-dollar GTX660, but the rest don't seem to care. Actually, the CPU (dual-core, 2006) is now the bottleneck.