Is he/she an auteur type, where you always know it's them? Or are they more of a chameleon, just there to serve that specific story in that specific way?
Do they write and direct? Or do they mainly do one or the other?
It's hard to choose a favorite, but Charlie Kaufman (who mainly just writes but directed one of his films which happens to be my favorite of his) has had a very large personal impact on my life.