When comparing Gitit vs MediaWiki, the Slant community recommends MediaWiki for most people. In the question“What are the best multi-user wikis?” MediaWiki is ranked 2nd while Gitit is ranked 4th. The most important reason people chose MediaWiki is:
Mediawiki is a widely used wiki engine. It is used to power Wikipedia and thus most people will be more comfortable/accustomed to using MediaWiki.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Lots of export formats
Giti has a multitude of formats that it allows to be exported, including LaTeX, ConTeXt, DocBook, RTF, OpenOffice ODT, and MediaWiki markup.
Pro Supports markdown
Getit supports markdown, a plain text formatting syntax that is designed so that it can be read by HTML.
Pro Free and open source software (FOSS)
Licensed under GPLv2 so you can download source code and customize to meet your needs, provided that you know or are willing to learn Haskell.

Pro Can be used collaboratively by multiple people

Pro Renders math
Using MathJax.
Pro The de facto standard
Mediawiki is a widely used wiki engine. It is used to power Wikipedia and thus most people will be more comfortable/accustomed to using MediaWiki.
Pro It has a powerful templating system
Pro Free and open source
Licensed under GPL.
Pro Version control
MediaWiki allows viewing past revisions of pages.
Pro It has a usable WYSIWYG editor
Pro Thanks to Wikipedia it is thoroughly documented
Pro Runs on any PHP server
It requires a webserver running PHP 5.2 or later of any kind.
Pro Great multilingual support
MediaWiki has full support for over 65 languages and partial support for over 300.
Pro Multiple database support
MediaWiki can store data in MySQL, PostgreSQL, Oracle and SQLite databases.
Cons
Con Requires Haskell
On some Linux platforms a binary package for Haskell may not be included in the standard repositories. So, it will be necessary to compile Haskell from source code or find a non-standard package repository, which may seem like a hassle if you don't use Haskell for anything else.
Con Access control requires an extension
There is no built-in access control, but you can download an extension for ACL.
