I think the main reason to check a convention website before a convention is for important convention updates (look at the Otakon front page, for example). I'd consider this sort of contest to be an important convention update, so.
It also helps that convention website URLs are a lot easier to memorize than FaceBook URLs.
Of course, I'm biased on this matter because I don't use FaceBook with any sort of regularity; I'm annoyed mostly because checking FaceBook for these contests is now one more different thing I have to remember to do when I already try to juggle remembering more things than I actually can (whereas checking the AWA main page and forums are already on that list).