in my opinion , joomla is better because it has so many extensions ( http://extensions.joomla.org/ ) and a perfect support forum (http://forum.joomla.org/)
Most Joomla 1.0.x extensions will work on Mambo, too with little or no adjustment at all. You need to put together the two projects that were once a single thing. Most valuable Mambo core devs moved away and so Joomla was born. Joomla is a vast and friendly community, I myself only touch Mambo when my customer who is requesting custom development work is using it. Other than that, I always go for Joomla when starting a new project. It's just that I see its future brighter than that of Mambo's..
i am not sure what Mambo is but according to my own thinking and guess Joomla was based on Mambo and i have always considered Joomla as a setup ahead of Mamboo (may be i'm totally wrong). I have't used Mambo but a fan of Joomla for its extensions and options available!
This means you are fairly new to Joomla! community. Here it is, the birth day After a major failure () in dividing power, reputation, copyrights and other stuff there at top, where a company called Miro International Pty Ltd was involved, old Mambo has been split in two parties. Obviously, one had to have a new name, so it became Joomla. Until Joomla 1.5 beta, M&J were pretty much the same thing, most extensions were cross-compatible etc.
Thanks Clive; i did't know about this history, i was just using Joomla for last 8 months for 2 of my sites!