They are completely different written from completely different code bases. Why don't you install both and see for yourself?
No, Typo3 Database management and abstraction utilities are greater. CMS is an extension in Typo3, there's a really big development API available to extend everything. I'm used to Typo3 though, but Joomla seems to be more popular in this forum so I guess it's worth the look...
Typo3 just didn't have enough support as in templates/modules/community support. I am sure it is great, but between the two my choice would be Joomla.
Joomla and Mambo were the same thing and even though they are not the same entity any longer - they are very similar - Drupal is quite different and not as user friendly.
For clients, if one didn't customcode, I would recommend Typo3. A lot of firms make their own flexible build of Typo3 and take it from there. Joomla is good - and I have seen very excellent sites using it. But in my book, Joomla doesn't power large commercial sites. But there are so many different CMS systems and setups available. You would (i keep repeating myself) be offered a lot better advice, if you gave some specifications on what you are doing/what you want accomplished.