Both versions offer a “Smart Delete” feature that allows you to find and delete duplicate media files while updating references to the deleted files, so that you don’t lose or break images on your site. But Pro is much smarter than the Free edition.
In the free version, this “smart” replacement functionality is only available for WordPress’s built-in featured image (aka thumbnail) fields — so when you delete a duplicate file that’s somewhere else, such as in the body of a post, it may be “broken” on your site.
The Pro version has been extended to also intelligently replace images in many other locations, including references in the post body, gallery shortcodes, and extra fields from WooCommerce, JetPack, and Yoast SEO. Using Pro makes it much less likely that a deleted duplicate will have a negative effect on your site!
The Pro version also includes dedicated support from the Cornershop team, as well as improved efficiency for accounts with a lot of images (in the free edition you have to babysit a progress bar as Deduper searches for duplicates; with Pro, it performs the search on its own).