The principal advantage is getting more sail area up high where there is considerably more pressure. Or more sail area without a taller stick.
The downside is greatly increased pressure on the battens, which necessitates their usually having fancy ball bearing cars and tension adjusters. And much greater leech tension for the mainsheet and vang to deal with.
Full battens often need crew help to clear the backstay and then in light breezes the battens will not flip, but remain inverted .... unless crew goes up the mast
and adjusts them ... they're very cool.