The whole ATK = high-end / STR = low-end was a theory that someone had and has been debunked.
One of our LNCs has been doing some STR vs ATK testing on L50 mobs and demonstrated over hundreds of autos and WSs that both STR and ATK can affect min and max damage, and that, point-for-point, STR is more valuable than ATK (against L50 mobs). However, in materia, ATK is available at close to a 2:1 ratio. Our testing is still in progress, so I haven't added any definitive notes about what's better than what.