I had to vote "other" because I need them both.
I hang blouses, skirts, pants, dresses, blazers and jackets. I can't imagine folding them up and having to dig them out everytime I wanted to wear something.
I fold t-shirts and pullovers, sportswear, and especially knits. Knits will stretch out if they hang for too long.
Right now, I have one closet with a couple of wire shelving units for anything that gets folded - underwear, pyjamas, as well as the other stuff mentioned above. It's all neatly organized. I wish the closet was a little bigger, to make more room for shoes and bags, since the shelving units have taken up that floor space.
DH also uses a combination of hanging and folding. His dress shirts and business suits need hanging, but he also wears a fair amount of "business casual" sweaters etc. that fold.
DS uses only drawers/shelves. For a teen boy, it seems to be more likely that clothes will get put away if they can just get tossed in a drawer or on a shelf, rather than take the extra step to hang it up.
DD has a single wardrobe unit with a hanging bar and a several shelves/drawers that work really nicely for the hanging/folding options.