My current 5770 has done well, but it has one seriously annoying flaw that I'm terrified I'll run into on the 7970: stuttering/judder in fullscreen. The FPS will be rocksteady according to every counter I throw at it, but there's a noticeable (to me) stutter in many games at fullscreen. Windowed mode, it goes away.
Just out of curiosity (and apologies if this seems patronizing since no one else asked), do you use Vsync in games? I remember that in Saints Row: The Third for example I had ridiculously bad tearing after switching to full screen mode before remembering to turn Vsync on in the settings (which I hadn't switched on from the start because I'd been playing it exclusively in windowed mode).
Alternatively, have you tried "forcing Vsync" in the Vision Engine Control Center (actual option is "wait for vertical refresh" with the slider all the way to the right)? If not it could solve the problem in some games that for whatever reason don't have a Vsync option in their settings (setting triple buffering might help as well), and if you have it might actually be the problem. Too many signals crossed and whatnot, particularly with games that run Vsync by default in full screen mode (probably not all that common for this very reason).
Just to throw this out there for anybody else following along at home who isn't quite sure what I'm talking about here (google can help), as long as you've got the hardware (ie: not Intel HD 2/3/4000 integrated graphics, any GPU over $100 can cover you here) Vsync is your friend in full screen mode, and if for whatever reason you still suffer tearing (look it up on wikipedia, you'll recognize it right away) try to stick to windowed mode. Most games with a decent budget (eg: the aforementioned Saints Row: The Third) will let you set a resolution which is just slightly shorter than your monitor's actual one so the bottom of the screen doesn't get cut off by the task bar.