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Wowpedia was created when Wikia screwed up royally by re-designing a globally imposed wiki skin without really accommodating the wishes of many wiki admins including WoWWiki. Instead of trying to work with the admins they basically said, "if you don't like it, leave." So many did. I mostly boycotted Wikia for awhile (6 or 9 months, I forget how long exactly) and WoWWiki was in bad shape soon after most of the WoWWiki admins made a copy of WoWWiki's database according to CC-by-SA and started Wowpedia based on that data. It largely happened also because Curse offered to host the wiki for free. I worked on Wowpedia and not WoWWiki early on after coming back from my boycott of Wikia, but I also worked on other Wikia wikis at the same time (like Templates and Logo Creation).
I didn't get along great with all the Wowpedia admins (even before they left for WoWWiki) and Wikia had learned from some of their mistakes. I also got to know Raylan13 who Wikia initially hired as a contractor to keep WoWWiki from falling completely into ruin. So, as I said I was still working on non-WoWWiki Wikia wikis, so I started checking in on WoWWiki from time to time and got to talking with Raylan13. Throughout this time I also took about a 6 month break from WoW (during Wrath). So when I got back into WoW I decided to see how WoWWiki was going and it wasn't good. Since I wasn't doing that much on Wowpedia by that time I started working again on WoWWiki instead.
I had plenty of disagreements with Wikia during this period and still we don't really see eye to eye, but Raylan13 turned out to be a really good person, so I decided to work on WoWWiki primarily to support him and give Wowpedia some much needed competition.
At least that's how I recall it. The order and timing might be slightly off, but that's the nutshell. I have probably answered this question half a dozen times, but I keep forgetting where I answered it.
Wowpedia is not really more popular than WoWWiki, but they do have a larger group of dedicated editors and admins. So, alot of their pages are better than WoWWiki. However, you got to remember about 80%+ of their content was basically stolen to start out with, so I would say on average Wowpedia and WoWWiki are comparable enough that you can't say one is definitely better tan the other. Most of WoWWiki's problems have been related to Wikia's mistakes. So, if they stop making them, WoWWiki may someday recover to it's former glory.
In all honestly, unless Wikia puts alot more effort into compensating for the huge mistake they made that led to the forming of Wowpedia, I expect Wowpedia to eventually kill WoWWiki.