I recently tried switching to displayport on my 6870 + Dell U2412M, U2211HM setup. With two displayport cables plugged in, my computer would not POST. It would power on for 1/2 second then immediately turn off. (This caused me at least an hour of panic. I had plugged the DP cables in without issue while the computer was running and hadn't turned my machine off for days...It took me a while to figure out what was going on.)
Apparently there is an issue with some DP cables (Startech and Monoprice specifically), where the power pin (pin 20) is connected when it shouldn't be. This causes problems with Dell monitors (and possibly others). The solution is to use OEM cables, or cables that are known to be wired according to the correct spec.
Anyway, it's probably a rare issue, but one of the wierdest computer problems I've encountered in recent years, so I thought I'd mention it. I returned the 10' Startech miniDP-DP cables I'd bought and have decided to stick with DVI for now.