The Two Towers is my favourite book, but it has been so long since I have seen the film that I can't remember if it is my favourite on screen as well. I really liked Return of the King, but got frustrated with it being so long. Putting all those factors together, at the moment I'll play it safe, and say The Fellowship of the Rings
I honestly did not like The Lord of the Rings trilogy, I've watched them numerous times because I love the genre and I want to like them. So every year or so, I give them another try. So far, my opinion hasn't changed. However, I loved The Hobbit: An Unexpected Journey. Thus far, it has been my fave by a long shot.