You can attach the Apple Thunderbolt Display to your Radeon board, the connectors are compatible, but you won't get a picture on the monitor. That's because at least the current Thunderbolt Display need a thunderbolt-enabled host system.
Maybe in the future, thunderbolt-enabled displays will be able to detect displayport video signals and show that on the screen, but we're not there yet. For now, this is an Apple-only monitor.
As for your question of how the LED Cinema Display will work, I don't really understand why you'd want to use that monitor with a PC. It has no additional video inputs and no on-screen menu system or buttons to control the same; you won't be able to adjust brightness, since that's all software-driven. Apple doesn't provide any stand-alone PC software for this task, only as a part of Bootcamp, which doesn't run on non-Apple computers.
I'd suggest that if you want a good 27" 16:9 2600*1400 pixel screen monitor you check out the Samsung S27A850D; its Super PLS LCD panel is said to be virtually as good as the LG IPS panel used in Apple iMacs and stand-alone displays, and it's noticeably cheaper too (by about 25% actually, give or take a bit.) Of course, you'll miss out on built-in speakers and camera (which aren't the best in the business anyway), but you'll gain a USB3 hub instead, dual DVI video inputs (plus Displayport) with picture-in-picture capability, and height/swivel/pivot adjustments on the monitor stand. The Samsung monitor's built out of plastic of course rather than aluminium and glass, but you're not gonna take it out on a safari anyway I bet, so I doubt that matters. It's a pretty stylish, industrial-design gadget, check out some shots on the web, I'm sure you'll like it.
