Obviously the general plot structure between the Quests' stories is the same: Kin and Gin sends either Jibanyan or Whisper back in time to a pivotal point in their lives with the intention of altering the timeline so that they never meet Nate/Katie. They then go through important moments in their past and near the end of the Quest, Kin and Gin confront them to try convincing them to change their fate. In particular, they have to decide whether or not they want to save a human close to them from death.
This particular choice is where the parallels somewhat diverge for a moment. Jibanyan chooses to stick to his fate - he loves Amy, and would literally die twice to make sure she stays safe rather than continue living as a regular cat without her. It’s not something he regrets, and the second time around he dies with the knowledge that Amy wasn’t apathetic or disdainful of his sacrifice. He’s barely swayed by Kin and Gin’s attempt to get him to change his fate.
Whisper, however, chooses to try and change Mitsunari’s fate, and his own in turn. Unlike Jibanyan, he’s much more easily swayed by Kin and Gin. He’s had a centuries-old wound reopened - he failed Mistunari - and he’s been given the chance to right his wrong. At first he’s upset by Kin and Gin’s appearance, but his regret combined with the knowledge that he’s not smart enough to help Mitsunari on his own is enough he needs to take their advice. But even with this newfound plan, it’s not enough. Mitsunari already knows that the battle is lost, but he’ll still fight until the bitter end.
Both Jibanyan and Whisper choose to save the human they care so much about, and in the end fate remains unchanged. The difference is in their success in their goals: Jibanyan chose to keep his and Amy’s fate the same and succeeded, while Whisper tried to change fate and failed.