I've played with both recently and can offer some insight, at least for Drupal 7.
The Wysiwyg module lets you use any number of editors, such as CKEditor. It also integrates with the Media module if you use that. If you don't want to use CKEditor, but, say, TinyMCE, then you'll want to use Wysiwyg.
The CKEditor module is (obviously) just for CKEditor, and has more options specific to CKEditor. For example, you can change the skin CKEditor uses (Office 2003, Karma, etc). You can also set advanced CKEditor config options which you can't do with Wysiwig+CKEditor. It also integrates with some file browser modules like CKFinder. And I believe you can use the Media module with new versions of CKEditor.
And I believe you can use the Media module with new versions of CKEditor.
I confirm CKEditor works with the Media module.
Here's how to enable it: http://drupal.org/node/1022986#comment-4403648.
By installing Ckeditor via Wysiwyg module gives you ability to select the tools you want to be default in a text format.
For example you don't want to show Image option in the default editor to users you can uncheck that in Wysiwyg module settings.
I use Wysiwyg + ckeditor + media to get the things done.