The $apply function can run on any scope, including $rootScope.
Are there cases when it makes a difference if I run it on my local scope or
Running $apply on any scope always results in a $rootscope.$digest. The only case where it might make a difference is when you provide an expression as an argument to $apply. The expression will be evaluated in the current scope (vs. $rootScope), but afterwards $rootscope.$digest is always called.
The source code is quite clear: rootScope.js
Bottom line:
If you call $apply with no arguments, it makes no difference.