Question: What is the difference between using the WYSIWYG module pointing to the CKEditor library and using the dedicated CKEditor module.

We currently use the WYSIWYG module with TinyMCE.

Answer: 
The answer seems to be that with [the Wysiwyg module](http://drupal.org/project/wysiwyg), you get an interface for which buttons appear in the profiles, whereas with just [CKEditor](http://drupal.org/project/ckeditor), you don't? Or at least it's not obvious where choosing which buttons appear happens in the CKeditor module. <http://drupal.ckeditor.com/> has some documentation on the subject, which says you can change the buttons. 

<http://drupal.org/node/606404> for some background on why CKEditor and Wysiwyg are separate efforts (though you can use CKEditor just fine with Wysiwyg).

I'd be inclined to stay with Wysiwyg so that you can swap out editors (that is, the JavaScript libraries for them) without having to swap out Drupal modules.
The CKeditor module gives you have much more granular control around where the editor windows appear, user role level permissions and the buttons available for each. The WSYIWYG API just allows for basic on/off configuration of editor windows for text fields across the whole site. Button profiles are based around input types (filtered & full HTML). The advantages of the API module is that it's not limited to just one editor (there's 10 or so) and really easy to configure.

The Ckeditor module is more difficult to configure and certainly not for most implementations, but very nice to have this module available if you require that level of control.