It's not your card, or your rig. It's the new ATI drivers, you're not the only one having issues, if you don't believe me do some searching on here & Google.
I went from 10.12 > 11.1, got constant display crashes, huge FPS dips, etc. I went from 11.1 > 11.a and got less frequent crashes, but it still crashed and I got huge FPS dips.
After attempting to fix everything up after the gigantic mess, I just got angry and reformatted. After reformatting I reinstalled 10.12 and everything went back to normal. No FPS dips, crashes, etc.
Oh, it also doesn't help that GTA4 is a horribly optimized game