The 380 flying long distances do rival the 340 on initial climb rates! RR fitted 380's certainly in high temps travelling long distances cannot meet a initial 5deg climb gradient and we have to give radar vectors. Mind you I am only talking recent aircraft types, I am lucky enough to remember Tridents and Flying Tiger 747's and that is a totally different ball game!! :-))
I have been lucky to be paid to watch aircraft either visually or on radar for the last 33 years and for the last six have worked at the biggest 380/heavy airport in the world.
P.S. Nothing and I mean nothing compares to an over loaded IL76 in high 40C's!!