We have been using both systems for over 7 years and there are pros and cons for both.
It really depends on what you need the website to do. I think that larger websites that are managed by several different users, like University Websites or websites with more than one editor should be programmed in TYPO3.
Smaller websites with one editor and a few pages that don’t need to be designed under corporate design guidelines can be less expensive if WordPress is used
For a test we did webdesign-orlando.com with TYPO3 and Webdesign-phoenix.com with WordPress after switching Web Design Phoenix to wordpress it lost 2 positions in its Google ranking but looks much better than before. Maybe we will switch it back at some point, since all the design features we are using in wordpress are available in TYPO3 too and the backend would be much nicer to use.
There are themes with good visual editor available that have many built in features
Blog features easy to use
Portfolio features easy to use
The menu editing much better is in TYPO3. Its all in one place and intuitively designed
Undo function or viewing of history is really good in TYPO3. You can see when who edited what and undo it for any element or page.
Duplicating elements or pages is a quick copy and paste in TYPO3
You can also copy and paste as alias: You can edit one main element on a page and all alias elements of this will be changed on the whole website.
Redirects are simple
You can hide pages or elements with one click, change rights of user groups that can see or edit the pages easily
Don’t need Child themes
Basically everything is possible in TYPO3 it might just be not a standard function.
You can have many websites in one installation, making it easy to update many websites at once and use custom global programming for all of them.
You can also customize the design for certain subpages of one page so that all of the subpages have the same design features. Pages that are dragged under a certain folder automatically all have the same look and feel.
Programming is much cleaner and the source code shorter.
Automatically switching elements on and of on a specific date not possible
Hiding elements is not possible
SEO optimization not as good as TYPO3
Editing an element you have to save the element you were working on and then update the web page too. (one extra unnessesary step)
It is confusing that the design settings are in several different places. The theme has settings, the wordpress installation, the plugin.. in TYPO3 its all in one spot.
If you don’t use a Theme with a good visual editor you will have to learn some HTML to get the website looking good.
Is targeted by hackers more than TYPO3
Blogging is not as easy in TYPO3 – but the news extension that works very similar is pretty nicely customizable.
There are almost no themes available.