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: 
From my experience, using the Wysiwyg module was a better decision.  

In some special cases (mainly when the editing was inside of an Ajaxed page), using ckeditor was a bad chioce.  

When using the Wysiwyg, replacing the editor itself wasn't a hard task, which solved several problems very fast.  

Therefore, for future situations you might not even think of now - use the Wysiwyg module.
Using the WYSIWYG module will allow you to fairly easily switch to another editor if you find one you prefer (or if new ones come onto the market).