Similar

• Both are full-featured free and open source web applications with which you can realize a very diverse variety of projects.
• Both are written in PHP and use a database such as MySQL
• Both can run on standard, inexpensive hosting.
• Both have large & vibrant communities

Different

• TikiWiki is more centralized. TikiWiki is the all-in-one model while Typo3 (like Joomla!) is the small-core-and-add-what-you-need model. Each model has its pros & cons.
• TikiWiki is Wiki-centric, whilst Typo3 is publishing-centric. Please see (if) Why Wiki Syntax Is Important to your project.
• Typo3 is GPL, TikiWiki is LGPL. The main difference between the GPL and the LGPL is that the latter can be linked to (in the case of a library, 'used by') a non-(L)GPLed program, which may be free software or proprietary software.

CMS Matrix

Compare them at http://cmsmatrix.org.

Alias

• Typo3