Jet, and Katara’s storyline parallels Zuko, and Katara’s storyline in Book 3—but, with a twist:
Both set out on a quest in the name of honor, caring little for the consequences of their actions. To one, honor means capturing the Avatar. To the other, honor means righting a wrong by holding a deep-seated grudge against those he deems to be the enemy, and doing everything in their power to fight them.
They both end up earning Katara’s trust…only to end up breaking it
Later, they earn Katara’s trust again.
Even though Jet swore he changed, he could never really let go of his grudge against the Fire Nation…and died as a an indirect result of this (If he hadn’t called Iroh out as a firebender, he wouldn’t have been dragged to Lake Laogai. If he wasn’t taken to Lake Laogai, he wouldn’t have been able to tell the Gaang its location. If Jet, and the Gaang weren’t underneath Lake Laogai, Long Feng wouldn’t have killed Jet.).
But, Zuko lived. Why? Because he was able to fully renounce his old identity, giving up everything to embrace his new life with the Gaang. And, in the end, he was rewarded for his noble actions.