There are a lot of episodes that highlight the parallel. :) I loved the sequence in The Awakening where Zuko and Katara were both being symbolically taken back under their fathers' wings. They did a magnificent job of contrasting the smothering, superficially civil interplay of submission and control masquerading as paternal affection between Zuko and his dark pater; and the loud, argumentative, confrontational, even teary, but ultimately open and loving reconciliation between Katara and Hakoda.

(And, yes, there's a fragment of Zuko's experience in each of them--Toph's escape from a life of porcelain, protected nobility that drove her crazy; Aang's feelings of failure in the past and determination to strive for honor and the good of the world in the future; Sokka's warrior upbringing. One of the aspects of the general ignoring-the-Gaang-Plus that especially disappointed me was losing the chance to see Zuko interact with Haru, Teo, and the Duke. Father/mother issues and learning to stand on your own two feet...physical scarring and learning to move beyond it...rebellion, repentance, and heck, knowing Jet...they had so much to talk about, but alas, it remains forever in the realm of fill-the-gap fanfic.)