I've used DADGAD for years. Advantages are the extra bass resonance you get from those open and detuned strings when playing in basic D position, and the elimination of those nasty thirds you're stuck with for most chords in conventional tuning. The sound is very open and sparse, and invites the use of drones, which suits traditional music but gives a fresh sound to other kinds of songs too. Martin's tunings do the same kind of thing, only more so!

Bad news is it can sound samey if you use it for everything, and if you like a lot of jazzy chords they're harder to find. But you can also use it in G position and A position (the latter works best for modal stuff) for variety, and it can sound good capoed up several frets for a more dulcimer-like effect.

The way I learned it was by trial and error. You can mess about moving the basic chord shapes up and down the neck, and just see what happens.