Fear and Loathing is one of my top 10 movies. I sometimes wonder if it's actually my favorite, since to this very day I find it to be one of the most re-watchable films amongst my favorites.
As far as playing a drunk goes, Raoul "Hunter S. Thompson" Duke is a significantly different performance than the swash-buckling Jack Sparrow.
Really I think what people are noticing is a consistency of what a director wants from him. He's worked with Tim Burton a multitude of times, and Gore Verbinski clearly has a certain expectation over what he wants out of Depp.
Let's not forget this guy also gave us Gilbert Grape, Chocolat, and Art of the Deal.