Catched errors in AngularJS's exception handler

Question

I have some piece of code dealing with promises that can throw errors. I tried to make a very small example showing the problem.

In both functions g1 and g2, we call a function f, which doesn't throw errors but can set an object err with an error:

let err;

function f() {
    err = new Error('error');
    return $q.when('ok');
}

// First implementation
function g1() {
    return f().then(res => {
        if (err) {
            throw err;
        } else {
            return res;
        }
    });
}

// Second implementation
function g2() {
    const deferred = $q.defer();
    f().then(res => {
        if (err) {
            deferred.reject(err);
        } else {
            deferred.resolve(res);
        }
    });
    return deferred.promise;
}

g2().then(res => console.log(res))
    .catch(err => console.error(err));

I thought the two implementations would give the exact same result, but there is a difference. I also have an exception handler to catch all uncatched errors in my app:

angular.module('myModule').factory('$exceptionHandler', function () {
    return function (exception, cause) {
       console.error(exception);
    };
});

When calling g2, since the error is catched, the exception handler is not called. But it is the case when calling g1: I obtain a first log from the exception handler, then a second log for the catch function.

Would someone have an idea about this difference of behavior? I think the syntax used in g1 is much easier to write and read, but I also don't my errors to be thrown twice...