Why were both appropriate in their era?
You’re being asked to compare, for example, the Dellsarte style vs. the Stanislavski style. In external acting like Dellsarte, the actor poses and puts on a facial expression to convey emotion. In the internal style, the actor is supposed to actually generate the emotion that the character is feeling, and the posture and facial expression is supposed to appear more or less naturally.
I’ll note that there’s a lot of confusion about these styles. The very best external technicians wind up feeling something emotive while they’re posing. Internal-method proponents sometimes find that assuming a posture and an expression can trigger an emotion. Psychologists have known for a long time that our external appearance can affect our internal mood–if I force you to sit in a slouched position, head down, chest caved in, you will likely start to feel a little depressed. So there’s less of a sharp division between the styles than many would insist.
Why was each appropriate to its era? Because audiences come to expect certain styles of acting. If we could transport ourselves back to Athens about 2500 years ago to watch one of their plays, we might not even recognize it as a play–rather, some sort of ritual (which, in fact, it was derived from). Watch some Kabuki plays sometime; that’s external acting, and to our contemporary Western eyes that are culturally accustomed to internal acting, it’s wierd.