CMS migrations are necessary when security support for an old version of CMS software is discontinued. Because these websites usually have a number of third party extensions or templates/themes installed each case is unique and requires research to determine the best path to successfully update the software to it's newest, fully supported version.
Here is are the dates where security support for key Joomla and Wordpress versions have been discontinued in the past:
Last version: 1.5.26
Support discontinued: September 2012
Versions after 1.5 offer 1 Click Upgrades!
Last version: 2.5.28
Support discontinued: Dec 31, 2014
Versions offer 1 Click Upgrades!
Wordpress implemented automatic updates back in 2008, with version 2.7. so migrating the data to newer version is not usually a big problem. Wordpress plugins and themes, however, can to have a short lifespan a may break when an older installation is updated to the newest version, especially if they are no longer supported.