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 $digest/$apply on any given scope will visit all other scopes using depth-first traversal:
https://github.com/angular/angular.js/blob/3967f5f7d6c8aa7b41a5352b12f457e2fbaa251a/src/ng/rootScope.js#L550-L558
That means that the only difference is that the $digest will start at whatever $scope it was called on