I have seen both angular.factory() and angular.service() used to declare services; however, I cannot find angular.service
anywhere in official documentation.
The factory pattern is more flexible as it can return functions and values as well as objects.
There isn't a lot of point in the service pattern IMHO, as everything it does you can just as easily do with a factory. The exceptions might be:
Arguably, the service pattern is a slightly nicer way to create a new object from a syntax point of view, but it's also more costly to instantiate. Others have indicated that angular uses "new" to create the service, but this isn't quite true - it isn't able to do that because every service constructor has a different number of parameters. What angular actually does is use the factory pattern internally to wrap your constructor function. Then it does some clever jiggery pokery to simulate javascript's "new" operator, invoking your constructor with a variable number of injectable arguments - but you can leave out this step if you just use the factory pattern directly, thus very slightly increasing the efficiency of your code.