I asked this question a few months ago after watching a couple of A 380s departing LHR , in both cases the SID required a significant turn away from runway heading and I had a reply from an Emirates pilot who said that its initial climb performance is not spectacular but ti soon gets going after a few track miles.
Perhaps this is not surprising considering its heritage where the A340 allegedly only got airborne because the earth is round-ire Airbus do not put more power on the wing than they need. This of course leads to the other point that as it has four engines it doesnt have the excess reserve of power a twin needs to climb away after an engine failure. Watch even a heavy 777W (300) depart and it will still climb impresively even ona long trip.
As to 747s I am not sure they perform much better than the 380, a long haul to say Capetown or Singapore sees them rotate well down the runway and climb out at a steeper deck angle than climb angle for some time.
Like you though I have been interested to watch the 787s , as a twin one would expect an impressive rate of climb but that does not seem to be the case with some very shallow climb outs from LHR and most of these aircraft do not yet operate on the really ultra long routes but their performance appears very modest-again due no doubt to some serious derating.
So it seems both new boys (I know the 380 isnt exactly new) trade climbout performance for either or both fuel economy and noise ina more sophsiticated way than their predecessors.
Now if you like real climb out performance you are too late and the last of the SAS MD80 s has sadly left LHR for good and they can no longer be seen as their tiny wings and sooooo long bodies made the intial climb angle look even more impressive.
PB