I upgraded from an XFX 6970 to a MSI R7970 Lightning running at stock speeds (1070 MHz). Prior to the 7970 I had no crashing issues. Now I'll get a Grey Screen of Death about every other day. Usually it'll occur after the computer has been on standby i.e. I come home from work, wiggle the mouse, open Firefox, GSOD. It's usually a predominantly grey screen with evenly spaced dark grey vertical lines all the way accross the screen. Let's say my browser was already open. I'll type in a URL, hit enter and then the crash will happen. It also won't happen every single time I come home from work, sometimes two days, sometimes three, sometimes immediately the next day.
I'm currently using the 28 June 12.7 Beta release drivers. I haven't tried to roll back yet to the WHQL 12.6, but I was going to. Any ideas outside of that would be helpful.