Ok, I had a chance to try out the new 6.05. First, my card (1080 SC) was already supported by 6.04, so that wouldn't be different for me. It actually looked exactly the same to me (in order words, like a gimmicky toy program instead of a real tool). So the real question here is whether, as the OP asks, one will get higher performance with this new version.
 
My 1080 SC could run the Heaven benchmark (was on 1440p for another thread, even though I have a 4K monitor) at 2152 Mhz, but it would show video artifacts every few seconds. I fired up 6.05, made sure my settings were the same, and ran Heaven again. At first I saw no artifacts, but the temperatures were low (around 40 C) so I had to run it two or three times to get the temperatures up to the equilibrium temperature of 49 to 50 C. By the time the temps hit 49/50 I was seeing artifacts every few seconds.
 
So, at least with the limited form of testing that I could do, doesn't reveal any difference in performance for my card.
 
As for the difference between Afterburner and Precision X OC, I couldn't say, because I haven't run Afterburner since I water-cooled my 1080, which greatly improved its clockability.