Differences between using a method reference and function object in stream operations?

When using Java 8 streams I often find that I need to refactor a multi-statement lambda expression. I will illustrate this with a simple example. Assume I have started writing this code:

Stream.of(1, 3).map(i -> {
    if (i == 1) {
        return "I";
    } else if (i == 3) {
        return "E";
    }
    return "";
}).forEach(System.out::println);

Now I am not very fond of the large lambda expression in the map call. Hence, I want to refactor it out of there. I see two options, either I make an instance of Function in my class:

private static Function<Integer, String> mapper = i -> {
    if (i == 1) {
        return "I";
    } else if (i == 3) {
        return "E";
    }
    return "";
};

and use it like this:

Stream.of(1, 3).map(mapper).forEach(System.out::println);

Or I simply make a method:

private static String map(Integer i) {
    if (i == 1) {
        return "I";
    } else if (i == 3) {
        return "E";
    }
    return "";
}

and use a method reference:

Stream.of(1, 3).map(Test::map).forEach(System.out::println);

Apart from the obvious matter of taste, are there any advantages or drawbacks to either approach?

For example, I know the stack traces become more readable in the method reference case, which is a small advantage.

via Chebli Mohamed