I know all about how the different connections, being digital in nature, are going to be pretty much identical.
That said, I prefer Dual Link DVI-D for anything up to and including 2560x1600. I just see HDMI as a home theater interconnect, rather than a PC one. That, and I have yet to find an HDMI cable that is as well built as the Tripp-Lite 20AWG O2-free long-strand copper quad-shielded DL-DVI-D cables I use for my monitors. Since I do audio production, unlike 99.9 percent of people I actually have to pay a brief glimpse of attention to ensuring that signal interference is a non issue. I am quite organized with my cabling, perhaps even a bit OCD, as I have sleeved every external cable and wire, computer/video/audio/network, with the extremely high quality and effective yet very affordable TechFlex EMI/RFI resistant copper mesh sleeving (followed by a layer of non-metallic resistance sleeving and topped with Kevlar+Aramid ultra high density protective sleeve). It is not something that I think is needed or even beneficial for most, but with a few thousand feet of cable/wire, there are going to be less than ideal crossovers regardless of how exhaustively laid out the cables are.
So, I would say that the high quality (=/= high cost; the Tripp-Lite 12/15 ft cables are $14-21/ea) DL-DVI-D is more for peace of mind than anythingelse.
That ssaid, I did find that when I switched from the Monster (I was given them free) DVI cables to the current ones, I now have the ability to overclock displays that were previously completely unable to run at any higher refresh rates than stock. My P2212Hb, for example, will clock all the way up to 92hz without dropping frames (using a friend's high speed camera capturing 600fps), so while I think that the high refresh rate monitors are more of a gimmick than anything else, I won't complain about running 75hz instead of 60.
My IPS/PLS WQHD/+ displays, also, seem to have an extra 1 percent wider color gamut under Adobe RGB, as determined via two decently high end hardware calibration devices. That could, however, be merely a coincidence, say from the panels having "broken in" over time.
Put bluntly, I don't see HDMI as anything other than a parallel technology to DVI, but while the latter is designed for computers, the former resides in entertainment centers and living rooms. The HDMI tech at present simply doesn't have anything to offer over DVI, with very few exceptions (ie for an HTPC feeding a receiver, it is a much better choice).
Displayport, IMHO, is the true spiritual successor to DVI, but it is taking its time getting off the ground. It, unlike HDMI, has the capacity to fulfill it's promises of hugely increased bandwidth, along with quite a few other promising bits with regards to implementation.