MediaWiki is an important competitor, because it is the first choice of a lot of companies.
MediaWiki has probably the biggest market share, not only for public, but also for enterprise wikis.
But MediaWiki is also one of the weakest enterprise wikis, because does not support most of the essential features an enterprise wiki needs. MediaWiki-users are most likely willing to change wiki-engines. We want to show them that Foswiki is the right software to switch to.
Strengths
Faster than Foswiki
Everyone knows wikipedia, the primary MediaWiki instance.
Parser functions extension and other extensions greatly enhance its functionality
Community discussion and offline interaction is simplified due to the following features:
Comment associated with every edit
Discussion pages for every topic, including user pages
Watchlists
Convenient user interface to see a user's contributions. Can more easily find related edits and gain a sense of the user.
Convenient user interface to see the differences for each revision to a topic; can compare to the previous edit or to the current version. This makes it easy to catch up on what discussion has gone on while you were away.
Weaknesses
Does not support spaces or wiki-webs. Is that possible through extensions?
Does not support tables in an easy manner.
Wikipedia does support tables that, from a user's perspective, is quite easy to use.
Does not natively support any rich-text-editing (can be changed with a Plugin, though).
Does not support attachments, only uploads (which are less convenient).
Though some access mechanisms are supported, does not support mechanisms that make it easier to manage restricted access to a broad set of topics, such as access control lists and groups. (Foswiki has as powerful Web- and Topic-Access-Limitation available.)
SMW apparently doesn't have a convenient way of doing queries that is the equivalent of Foswiki nested searches - discussion here