This is an interesting matter and something I feel strongly about, so I'll elaborate upon my views here.
I absolutely believe BS01 is the superior source of reference. Here's why.
BS01: The front page here is incredibly consistent and immediately Bionicle. It's very friendly and open, and has eye catching images to get you started. You can dive into the Bionicle lore almost immediately upon entering the website, and the look is clean enough so you don't feel too over-crowed. Maybe it's just me, though.
Everything is laid out very nicely, and it's enjoyable to look at. Everything is very clean and uniform, and allows for easy navigation and page surfing. I really enjoy how this is spread out. The colors are also very relaxing, so I'm happy to roam around looking at the articles of story.
Wikia: The front page here is very standard for Wikia's. Now, this isn't really a bad thing, but this isn't spectacular either. The colors are really unusual and to me, quite uninviting. Also, instead of providing me with a quick way to access story information, they immediately direct me to other wikis and affiliates of theirs. I see they are trying to spruce up the way the front page looks, but the colors just seem too far apart and too randomly placed for me to appreciate the effort. It instead comes off as being really poorly done.
When they do get around to Bionicle information, it's oddly placed as well. The featured character/page, sure, but then it's broken up by wiki related articles. It's really unusual and not a very friendly layout, at least not to me.
BS01: For this, I'll compare the two Wiki's Gali pages. On BS01's, the Gali page is laid out very clean and concise. You have a really great function on the right that allows you to sift through the bare-bones information on the character through out her three different forms - Mata, Nuva and Mistika. You see her Nuva Symbol as well, and it isn't messy in the least. Everything is easy to read and the page is vibrant and interesting.
The page goes on to catalog the characters history, and does a fine job of it. All the articles, this included, are quite well written. You feel as though you're simply reading a third-party synopsis, and that allows you to enjoy reading it as well as relay information to the reader better. A criticism I heard about these pages is that their aren't enough pictures on them. Comparing the pages, BS01's Gali page has 13 pictures not counting the three on the rotating info-table. Wikia has 6, with one repeated from their info-table.
Wikia: The wikia page for Gali also has it's info-table, but only shows the most recently released version of Gen1 Gali. You can't switch between the three forms, and the immediate impression I got was that this looked very boring. The information present below the image is unusually long winded, and you get a lot of unnecessary information thrown at you right off the bat. You have to either know of these things or ignore them for now if you're just getting into the story. It's also all in italics, which isn't really bad, but not pleasant to read here either.
The written content on this (as well as others) article is unusual. Sometimes, it's really detailed. Other times, it isn't. It trades off and, compared to the BS01 page, leaves out a lot of information a lot of the time. If you can't get ahold of books or comics, coming to the wikia will sell you short for information and details you may have wanted to know. The writing itself is also odd, feeling more like it was written by someone trying to tell you about Bionicle, as opposed to a third party chronicling it. A lot of the time, there is also what appears to be speculation or out of place information, especially in the trivia section.
BS01: Navigating BS01 is very easy. On this character page alone, you can see images in the upper right where the character was seen and had a presence. This allows you to travel to the story page for that year. At the bottom, you have the navigation tools for the Toa team as well as the years that character was a set. And then below that, you have an over-all navigation for the rest of the pages.
Wikia: You get a fraction of what was written above. You do get the bottom navigators, but oddly specific ones such as Mistika and Phantoka (terms not used in the story) and over-all Toa of Water. The latter makes sense. The former does not. Finally, you are contained to that pages relevant content. No over-all navigator. You do have the category links, but those don't take you to anything quickly.
BS01 is simply better in every way. It's trustworthy, easy to use and navigate, and well-written and laid out. The only reason I can see people having for using the Wikia over BS01 is habit, or a connection to the site.
And those are my thoughts.