Legendaries in the anime are completely different than Legendaries in the games. In the anime they're much more like gods, treated as such, and have a ton of legend surrounding them. Additionally, they're also much more powerful in the anime. Your Dialga might be strong, but it might not be able to take down the Elite Four by itself, while in the anime it probably could.
The legendaries in the anime also tend not to attach themselves to humans for a long time, like in HGSS Suicune follows you around and in basically all the games where somebody says "it's been waiting for someone like you to catch it." They're much more... closed off.