From my own experience as an ATCO, general initial cruising altitude for wide body twins goes 767<777<330<787=350. Cruising speeds 767<330<777<787=350. I certainly see the 777 match the newer twins when the 777 isn't operating ULH but obviously she needs to burn more fuel to do so. Fastest I've had a commercial widebody so far was a B744 at M.090 with a medical EMG on board. I have had a B744F at FL450 once, asked them how they got up there, she was an empty positioning flight. The descended shortly after as their ground speed was higher and fuel burn lower at FL410 with a big tail wind.
I always assumed the reason the 330 gets up there so much earlier than similar vintage Boeings was that the wing needed to take all the extra weight of the 340, so when on a lighter 330 it was almost overkill. Seeing how shockingly slow the A343 in particular climbed backed up that assumption in my head