git diff between two branches when the path has changed
Solution 1:
Git has no real notion of moved/renamed/copied files, however it has heuristics to try and detect those cases and then display them in a nice way.
That said, you can instruct git-diff to use those heuristics to detect renames by passing it the -M flag. With that you can try
git diff -M new_branch -- new-path/file old-path/file
and see if it works in your specific case. Further, git diff -M --stat new_branch will give you an overview of the changes, and also show you what renames Git's heuristics picked up.