Depends upon the quality of the PSU. Weak 600W will be same as 300W quality.
Weak: All is counted as total. Corsair, Enermax atleast count ONLY 12V rail outputs to the marketed total.
2x6770 sucks about 220W, my CPU (even tho it's extreme series) prob around 130W, and rest prob 50W. and GPUs and rest don't enjoy even solely 12V.
In any case, they are now running stable on the *same* system, in crossfire. Kind of, still reports 2 adapters, yet i got crossfire enabled. Whatever, is not crashing anymore. (Not needed for gaming). Next week 2x5970 arrives anyway and got to upgrade PSU, hopefully some store will have 1kW enermax in stock
Oh and quality differs: 550W cheapo PSU was not able to power up a system which a really old Enermax 350W was happy to powerup
I think that system required something like 450W and the really old, too small Enermax didn't have problems with that