A wiki allows you to organize stuff in order and not have it get buried. You can use forum folders with categories, but you can't change the order of things within the folder very easily, so you end up with stuff posted in the random order you created it.
I suspect a wiki uses less system resources than a folder, too, so that is an issue for the site as a whole.
Finally, if you use the same campaign world for multiple games, it's much more convenient to have that in a linked wiki than re-post stuff in each game you create.
No one's likely to look through your wiki anyway unless it is linked to something, so there's no need to worry much about spoilers. You're not going to put serious spoilers anywhere on either a wiki or a forum anyway, except if you store character sheets for your bad guys on the site, and those can be made private.