First comes SharePoint,

SharePoint! A Microsoft product you either hate or love. Microsoft states,
Your organization can use Office SharePoint Server 2007 to facilitate collaboration, provide content management features, implement business processes, and supply access to information that is essential to organizational goals and processes.
I partially agree with that statement. I think SharePoint can be a great tool for document repository. As for collaboration, it works for a small team with minimal documents. When used appropriately, SharePoint is also useful for content management. There are powerful features of SharePoint; the problem is that it is not intuitive. You almost have to be a SharePoint expert to appreciate all the SharePoint capabilities. Oftentimes documents are buried under multiple folders. It is difficult to get a dashboard view of the projects and documents housed in SharePoint. Bottom line, SharePoint is not the Holy Grail.

Then comes wiki …

Now we’re talking collaboration. Wikis are designed from the start for participation. Wiki is defined as a web based social collaboration tool that allows anyone to edit and contribute content. Wiki allows users to freely create and edit Web page content using any Web browser. Usually, editing a wiki space is just a matter of clicking the edit button on any page top or section header, much simpler than track changes in Word.doc or editing via SharePoint.
Wikis provide a platform for people to work together, build knowledge, and make connections. Like anything, wiki has its limitations also. Although we are now seeing more plug-ins for open source wikis to enhance features. Currently, there is no way of directly embed PowerPoint slides into the wiki. A way around it is embed PowerPoint slide into Slideshare, then embed Slideshare in the wiki. Same thing with videos, it needs to be embedded via YouTube. Doable, but could be better. Click here to see some great ways companies can use wikis.
Overall, wiki is a great tool for open collaboration while SharePoint is a great tool for document repository.