They all display up to 2560x1600. The difference is HDMI and DP carry sound while DVI does not. Otherwise between HDMI and DP there should not be a difference. I would go with HDMI because the cable is probably cheaper than DP.
You probably won't notice the difference, but that monitor purports to support 'xvYCC Compatibility' and 12-bit per channel internal processing (not sure if that's true 12-bit support of the billions of colours would infer) or just a look-up table for colour rounding. So with the ATi card you have support for 12 bits per channel xvYCC colour through HDMI 1.3 , while the DVI and DP connections are capped at 10 bits per channel.
However I don't really think it can truly display the colour gradients to make the most of that support, but if there were to be a difference, that would be the biggest one, even the audio differences doesn't really apply since the audio soundbar add-on is optional and not driven by the HDMI or DP audio.
"HDMI is intended as an external consumer electronics connection for HDTVs."
"DisplayPort is the digital interface for connecting flat-panel displays to computer systems."
"HDMI is based on legacy CRT raster-scan architecture. DisplayPort is designed for modern flat-panel displays and PC chipsets. DisplayPort has a micro-packet architecture with low voltage signaling that more easily enables networked displays. In the future, DisplayPort will also allow daisy chaining displays at full graphics performance, including 3D. and content protection."
Read the rest for yourself.
I've just bought Dell UltraSharp U2412M 24" eIPS with DisplayPort and no-hdmi and was researching around about this subject and also got here and elsewhere. Just leaving some feedback.
DisplayPort is a connection similar to the HDMI in the respect that it can also carry, on a single cable, digital video and digital audio, supports eight channels, has 24-bit resolution and a 192 kHz sampling rate, just like HDMI. While HDMI is targeted more towards consumer electronics, DisplayPort is targeted more to computers. Another important difference between the two is that the DisplayPort is a royalty-free standard, while manufacturers that want to use the HDMI connection must pay a royalty fee for each product sold. It supports its own copy-protection protocol, DPCP (DisplayPort Content Protection), and since its 1.1 version, also supports the HDCP protocol. It supports 4K resolution (4096 x 2160) and 3D video, just like HDMI 1.4. DisplayPort is very similar to HDMI 1.4, except that HDMI 1.4 supports a Fast Ethernet connection. On the other hand, DisplayPort has a bandwidth of up to 21.6 Gbps, while the bandwidth of HDMI 1.3 and 1.4 is 10.2 Gbps, leaving “space” for future features and resolutions.
One advantage of DisplayPort over HDMI is that it allows the installation of up to three video monitors to each port. In order to do that, you will need to use a DisplayPort hub connected to the video card, and the video monitors will be connected to the hub. Optionally, you can use a video monitor that has this component embedded, so you connect this monitor to the video card and the other two monitors to the ports available on the first monitor.
There is a miniature version of the DisplayPort connector, called Mini DisplayPort or simply Mini DP.