Well, first mediawiki is actually being used by the wordpress creators
(automattic) for their developer documentation as proof of powerfulness of its features.
Then, because the business model of mediawiki and wordpress are completely different.
Wordpress allows an easy use but as soon as you want to expand or complete your
website you are pushed (or constrained) to paying solutions.
Mediawiki (as well as our platform) is completely free, including any desirable
advanced feature, at cost to deal yourself with the code (starting from wikicode
itself, and proceeding with the creation of dedicated extensions).
Then, because the intrinsic anti-immediacy of mediawiki force at the quality of contents:
dealing with wikicode (either entered through the help of visual editor, or not) on the one
hand slows down the content creation, and on the other provides you with a powerful set of
formatting and structuring tools.
Then because mediawiki offers a strong versioning controlling and allow a collaborativeness that wordpress is not able to offer: many people can work on the same content in the same time, and notwithstanding the integrity of the content is preserved, and you can access all the changes made by each of editors at any time.
Finally because through the general design of our platform (where mediawiki is used as backend site) the presentation of the content (i.e. the appearance of the website) can be completely decoupled by the content itself: a part of your team can solely take care of contents, and their structure or pages structure, and another part of the team can design a frontend solution which will queries the APIs, and to consume those content in any way, using the semantic data container therein. (unless you are ok with the frontend solution here proposed)