... that was a difficult one to answer...
I'd say Bionicle G1 sure had a lot of memorable characters, but I personally never cared much about if those characters appeared again in the story - although I have to admit that it was kinda awesome to see the Toa Nuva again after 5 years. It also probably wouldn't affect Bionicle at all if only new characters will appear in the future, so characters can't really be the core of Bionicle as a whole.
The sets - G2 failed because it had a bad story, bad characters and no sufficient worldbuilding - it had good sets, though. Sure, if you like the sets simply as sets that look cool and are nice to play with, this could be your core of Bionicle, but I doubt that treating it that way would ever create a lasting affection to the line since at some point you either stop playing with the sets or get too good at MOCing to take much interest in the actual sets themselves anymore.
Some years ago my cousin visited us with his parents and when he saw my Bionicle collection he asked me if I had the "Yellow Destroyer". It took me a few minutes before I figured out he meant Hewkii Mahri. He knew nothing else about Bionicle, so I wonder - could it still be called Bionicle that way? And I think not, which is why I can't see the sets as the core of Bionicle.
Story and worldbuilding are strongly intertwined in my opinion. Some sort of backstory just is essential for good worldbuilding - especially when all we have is action figures. As I already said before, sets simply need some kind of backstory to work as a big thing. Why I still don't think the story is the core of Bionicle is this: However much the story influences the world, even more does the world influence the story. The story tells us why certain things are, as they are, but the worldbuilding tells us how they are. What can happen. Also it's the world that enables you to make up your own stories in a believable way.
I think I was pulled fully into Bionicle by a simple strip of paper included in a box of cereal or something - all it did was showing all the '01 masks and telling me what their powers were. And this simply added a meaning to everything. From there on Bionicle figures weren't just weird guys who could move their arms up and down anymore, but actual characters, simply because I suddenly knew something about them beyond their name. Then came the island of Mata Nui - some exotic place where the characters could have adventures, and only then did I actually learn about the story. This together made me buy the sets and once I had them I began to care about the individual characters beyond their individual looks.
In the end I'd say that everything together makes up a good theme, but worldbuilding really is the core of everything.