Whilst I agree with A320 fan that Aeroworld mentions nothing with respect to any comparison between the B777X and A340-500/600 involving the number "20%", DeltaAir is not far off the mark.
Boeing literature suggests that the B777-200X will have 7.5% lower trip costs, and 15% lower DOCs than the A340-500 on an 8,500nm mission. The lower DOCs primarily come about because the B777-200X can carry more passengers in a like-for-like configuration.
Boeing also suggests that the B777-300X will have 5.5% lower trip costs and 17% lower DOCs compared to the A340-600 on a 7,000nm mission. This is mainly attributed to the -300X being able to carry 34 more passengers in a like-for-like configuration.
I stress, also, that whilst Boeing does project these numbers, the manufacturer DOES NOT guarantee them, nor should they. Each airline has a particular mission for any particular aircraft type and operating costs are decided upon that. And, regardless of what others say on this forum the airplanes really don't have to fly before we can correctly find out about them as they are derivative airframes.
Airbus literature suggests that A340-500/600 operating costs will be lower than the B777X, and I'm sure that in a certain configuration they would be.
As far as DeltaAir's 20% figures go, however... not far off the mark, but in reality about twice the size of what will be reality.
Boeing will not launch the 747X at Asian Aerospace 2000. Phil Condit has already said that the airplane is not likely for anything close to a launch before 1Q 2000.