I use the applique stitch for needle-turn applique (as taught by the Piece O' Cake ladies). I hadn't heard of ladder stitch used in applique; it seems like it would be hard to do a ladder stitch as small as the applique stitch. I've seen whip stitch used in applique as a decorative choice when it's meant to be obvious.
I'd say for durability, nothing is going to beat the applique stitch.