On one hand it is the heart of Trinitarian reasoning. Persons are the “who” in a sentence that do the “what.” Natures are the “this-ness” of a perseon. Bottom-line: Persons do stuff, not natures. It has been a common Orthodox critique of Calvinist Christology to nail Calvin in his commentary on John 14. Calvin says that each nature (of Christ) does what is proper to itself. This seems to be a person-nature confusion. Admittedly, this is very sloppy language. However, the Orthodox can be guilty as well.
Many Orthodox say that human nature participates in the eternal resurrection ala John 6. The problem is that persons should do the participating, not natures.
My point is that both sides, while employing this necessary distinction, also fail it at times.