Services vs Factories in Angular JS?

They are pretty similar and in many cases can be used interchangeably.

Here you can read more about that subtle diferences: http://stackoverflow.com/questions/15666048/angularjs-service-vs-provider-vs-factory/15666049#15666049

From my experience I can add that since service is always initiated with the "new" keyword so it returns an object with values and methods. You can do that in factory as well (and in most cases this is what you want to do), but from factory you can also return an function. I found that useful when I wrote my own constructor function, gave it to the factory and then I could create many instances of it when needed.

// in main controller calling a factory constructor function that will create paginate with 5 posts per page
$scope.gallery = new Paginate(5, Model.stateParam(0), $scope.data); 

// in single post controller calling the same factory to create pagination for one post only
$scope.posts = new Paginate(1, Model.stateParam(0), $scope.data);

My paginate logic could be created in a service as well but would require a different approach to do so. I've found that this one works the best for my needs :) Just a matter of preference but staying on topic - this kind of initializing function with new would not be possible in a service.