I tend to think of them as a bit like the Time Lords from Doctor Who.
The Time Lords were capable of extraordinary things, but they had very few naturally ingrained abilities- some telepathic power and awareness, the ability to regenerate, some natural affinity for time and other dimensions... but that was, basically, it.
And yet they were arguably the most powerful race in the universe, even though all of their power only came from technology they'd mastered achieved over the eons. Their ability to control and manipulate time was derived from ancient technology, some of which was apparently half-forgotten even to them.
Like the Great Beings, the Time Lords made plenty of mistakes and had plenty of problems fixing those mistakes. (I could pursue this analogy further with some specific story references but I don't think it's necessary at the moment).
Or, to express this a bit more generally, it's the old "any sufficiently advanced technology is indistinguishable from magic" adage. That's what most of the other powers we've seen in Bionicle are anyway; protodermis-based technology that is so clever it may as well be magical. Since we know the Great Beings were creators, inventors, and tinkerers, it seems a reasonable assertion that all, if not most, of their "powers" are derived their own science as well.
Science which may very well be so alien to us that it appears magical, or at least completely impossible.