>>16190148The unique thing about those gens is that there is no single rival. There are multiple rivals with varying degrees of importance.
Gen III took the approach of filling the game with minor recurring rivals (Wally, the other player character, Gabby and Ty, etc.). None of these really fit the "proper" rival role, but I guess Wally is the closest thing to it. He's the last opponent you face before the E4, and he gets the most character development overall.
Gen V was much more character-driven than past games, which made all the rivals look like "proper" ones. But I'd argue that N was the closest thing to "the" rival, since he's much more central to the plot and the second-to-last opponent you face.