Well, I personally think the two shouldn't be compared, but I might as well speak my opinion.
While I did enjoy Bionicle's story a great deal, the open-endedness of Hero Factory's story allows for a great deal of customisation and implementation into the story; there's no limit to how light-hearted or dark you can make your story, which I think overall makes it a better franchise to get into and, oddly enough, gives it more of a "LEGO" feel. Although it can be difficult at times to create a unique character, the parts are generic enough to be used in very abstract ways (look up that purple octopus MOC thingy) and yet can still be used differently by simply rotating the piece on a normal set, which I think is quite an achievement.