I have installed ckeditor 3.6.6 and media 7.x-1.3 on a fairly new D7 site. When I add an image field with the regular image widget to a content type all is well and CKEditor works fine. If I change to the media file selector widget CKEditor no longer appears on nodes of that content type. After looking at some other posts here I unchecked the embedded media plugin on the Full profile in CKEditor module. But that had no effect. (I've cleared the cache numerous times).
I have been using the CKEditor module on D6 sites with no problem and on D7 with no significant issues. On the media project page there are instructions for setting up the WYSIWYG module to run CKEditor, but not any suggestions about the CKEditor module. I would rather not switch if I don't have to.
UPDATE: I have just started migrating content to this site and I found that when an images is uploaded to a node with an image field or a migrated node has an image file placed in the image field CKEditor is no longer visible. This occurs even after uninstalling the media module. If the image is removed CKEditor returns.