From what I understand of the forces involved (3 years of engineering, so don't quote me
), box stitching would be best if attached to a panel, whereas bartacking is better when attached to a reinforced edge or seam.
Bartacking onto a panel concentrates the stresses at the end of each bartack. If the bartack is on something that's designed to take loads, like an edge or seam, then it's ok, but if it's just in the middle of a panel it will eventually tear out at the stress concentration points unless you put reinforcing material behind it.
Of course, ideally the box stitching should be modelled with a finite element analysis program and then be stitched on in some wacky hyperbolic or elliptical transform shape