You're going to have a hard time matching his performance because the 580 is substantially more powerful than the 6970 (and priced accordingly). You do have a fairly high end rig though- you NEED to OC your processor. If you have the budget you could also consider getting another 6970 and 4GB additional RAM.
So i tried my friends 580 the other day and noticed the difference. When i put back my 6970 in i saw it had a switch on top. I researched and found out it had to do with flashing the bios. I ended up switching it to the other side to see what would happen. Wouldnt you know it, it played about as good as the 580.