The stuttering is with every game not just cs go. I feel that ive taken a step backwards by going with the 7950. My 580 ran smoother then the 7950 and its less powerful. I might go to bestbuy and buy a 560ti to test n see if possibly its something else in my rig causing it
Even if you aren't ocing, put powertune to max (+20%). I don't like the way that AMD does TDP throttling, compared to Nvidia. You can also try to turn vsync on.
If you are Ocing, make sure you don't have the ram too high. Supposedly w AMD, too high ram can run fine but be throttling itself internally. On some threads I see people don't get any more benefit past 1400 anyway.
I didn't have to do much to switch from Nvidia to AMD... just uninstalled the drivers, rebooted, and installed catalyst 12.6, and later on 12.7. I didn't try the 12.7b.