Hey, I just played through all of BFBC2's Single Player Campaign on Sunday (great game.)
The shadowing in that game is bad. This isn't a slam on the developers or anything, it is a console port by the way.
The LOD issues are there too. It isn't just a driver/card issue. I run a 5870 2GB on Cata 10.11.
On the flip side, Radeon's do have issues with shadows in certain games. Not sure if I just never noticed it or it popped up on a driver, but for example certain spots in World of Warcraft for me have shadow banding. It drives me crazy. I can flip over to the GTX 460 and suddenly those issues are gone. So, yeah.