At the most basic, the difference between the Incarnate and Therian Formes amounts to the same as the difference between Origin Forme Giratina and Altered Forme Giratina, Normal Deoxys and the other variants, and so on. That means that there is a physical change and a stats change. The “original” version introduced in the games was the Incarnate Version, but there is some dialogue in the original games that suggests that it is uncertain which is the “true” Forme and appearance: the humanoid Incarnate or the animalistic Therian.