Personally, when teaching newbies, I don't find Learning Perl that useful. Don't get me wrong it's a nice book, but I don't find that the order and emphasis of topics match the way I teach (e.g. I introduce OO and references quite early.)

I think Elements of Programming with Perl provides both more breadth and more depth than the Llama. Though I don't like everything about the book, it is the best beginner's book out there.