Unified and side by side diffs were never really meant for diffing documents. If you do go the route of introducing line breaks to improve readability and/or editing, you really need to use a different diffing algorithm. What I've found useful is the Google diff match and patch library.

http://code.google.com/p/google-diff-match-patch/

Its extremely easy to integrate as well. You can see how it handles a markdown diff at:

http://ny.testdrive.gitsense.com/index?#pid=23&cid=27&trail=