That DVI is probably a singlelink DVI, you need a duallink DVI cable to use on resolutions higher than 1920x1200. (Given that that resolution of 2560x1080 is a single screen). You can check it by looking at the pins of the cable. Are there pins missing? -> it's a single link.
Displayport, whether it would be mini or not does not differ, but that should be working out of the box, kablam, directly no problems whatsoever. However, I don't know why but it sure gives me problems sometimes as well. I just use dual link DVI cables for everything if I can to be sure everything works as optimal as can be.
Here is a picture to clarify what kind of DVI cables exist:
Note how the second one uses all pins available, which is DVI-I Duallink.