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The Joomla 1.5X series was one of my most favorite releases. It was one of the most advanced CMS systems when it was released, had an awesome MVC architecture that took development to a new level in Joomla & it was rock stable.
After the Mambo days, the Joomla 1.X series did a great job in maintaining the code but it was 1.5 that was the game changes in so many respects. However as with all technology, times changed & Joomla had to evolve too !
Out came Joomla 1.6 from which everyone had great hopes as it was the first major release after 1.5 which had done a great job & 1.6 had taken a long time coming. It introduced a full fledged ACL for the first time , One click updates, Nested categories & a lot lot more . It looked awesome on paper however just didn't cut it many aspects. Part of the problem was that a lot of things had been taken on at the same time & expectations had increased a great deal due to delays.
Joomla 1.7 came out fixing many issues in the 1.6 series & also started a 6 Month release cycle adopted from the likes of Ubuntu . With this & similar process changes, the project mitigated the issues that it had experienced with the 1.6X release cycle. Joomla 1.7 was however a 'Short term release' and more of a stepping stone to solve issues in 1.6 & serve asway to easily move to the Long term support (LTS) release of Joomla 2.5 when it came out.
The first 2.5X release when it came out had fixed over 300 bugs in the last version of 1.7 & was recommended to be THE version to use for new sites. It was strongly recommended that & all sites on Joomla 1.6X & 1.7X should be running on minimum Joomla 2.5X.
Overall I love Joomla 2.5. Its most deservedly an LTS & is very stable. A very deserving contender to Joomla 1.5's legacy of awesome features, great security & stability.
The Joomla 3X series in in my opinion the most ground breaking release that redefined the rules of the game once again after Joomla 1.5. From 3.0 to 3.2X , Joomla has seen the most rapid & stable feature development of the most awesome CMS features since its inception. I sincerely believe that the 3.2X release is the best Joomla that ever was till now ! With awesome feature additions like tagging,an awesome 'App Store' like one click extension install feature, great enterprise security functions like the Yubi Key authentication & to name a few - Joomla 3.2 seriously rocks.
Joomla 1.5 had its end of life in September 2012 & the last released version was 1.5.26. There was only one known security vulnerability which was fixed with this patch. Though there are no known issues with 1.5X now, it is still recommended that you upgrade as soon as possible to the latest LTS at a minimum.
My personal recommendation would be to go with the latest Joomla 3.2X release.
That would definitely not be a place i would like to be in ! 1.6 & 1.6 were both STS releases & do not get any security updates. Plus they have many bugs that have been fixed in later releases. So definitely definitely upgrade to the latest J! version.
Bottom line, Joomla is one of the greatest CMS's out there.. I purposely left out the 'Open Source' here.. Make sure you have the latest right versions, keep them updated to the latest release & enjoy the benefits of this awesome free CMS.