Obviously this kind of question can only be answered in depth by an amd engineer.However, simple part of this would be the fact that tahiti based cards are siginificantly slower to start with so they have less room to "work with" using mantle.So it can mean that it is in big part just from the fact that tahiti cards get saturated sooner and "the blame" shifts from CPU to GPU part.Have a look at this, its from the same site, just in this instance they set high MSAA to bring 290X down:
http://imageshack.com/a/img33/1289/wdoo.png
So when the GPU is being hammered down, mantle doesnt bring high gains even on GCN 1.1.But you have to keep in mind that hawaii has more computing power, it has faster memory access and was built in mind with mantle.
As i said earlier , this thing is gonna be hard to quantify, it will all depend on the hardware used, on the settings used, and even with same hardware and same gfx settings it can be almost no difference in scene where there arent LOADS of objects on the screen to a MASSIVE difference when there are thousands of them.Thats why i think amd works with starswarm, they want to have the capability to show what it CAN do.Lets remember that mantle isnt only for same games and same scenes like on dx just with less overhead, its also for things that DX ultimately wouldnt be able to handle.