Tiki vs Joomla!

Similar

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

Different

Tiki is more centralized. Tiki is the all-in-one model while Joomla! (like Drupal) is the small-core-and-add-what-you-need model. Each model has its pros and cons. Because of these design choices, Tiki has more features out-of-the-box. With Joomla, you can add numerous features via extensions.
- Tiki has all the features built-in (and you just activate/deactivate them); thus, every Tiki instance of a given version has the same code base. This makes it easier for a hosting company and for upgrades. In contrast, if you maintain dozens of Joomla! sites, they will have different modules installed depending the use case.
- When Tiki is upgraded, all the features are supported and the upgrade is smooth. In Joomla!, some of your plugins/extensions may have become abandoned or may be incompatible with the new version.
While Tiki is a very large and popular project (over 200 contributors to main code base and tens of thousands of installs), Joomla! is several times larger with millions of installs.
Tiki is wiki-centric, whilst Joomla! is more web publishing centric. Please check, if relevant, Why Wiki Syntax Is Important to your project.
- Joomla! uses MediaWiki for its own wiki.
Joomla! is GPL, Tiki 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.
Joomla! uses Mootools while Tiki uses jQuery.
For the last few years, Tiki has had a much faster release cycle than Joomla! but now, Joomla! is moving to a 6-month release cycle, like Tiki, Ubuntu and many other projects.