I haven't used or played with phpwiki, but I use mediawiki on a few installs. There were two main reasons for this.
1) Wikipedia is built on wikimedia
2) Wikipedia has a wealth of articles that users can view the wiki source of, then copy and paste to accomplish the same formatting in their own wiki.
The second one was huge as it allowed my clients to learn how to create wiki pages by example, rather then studying syntax. After a few pages it became second nature for them.
Boils down to, go with which ever is the easiest for you to learn, use and maintain.