I'm so glad the two characters I was rooting for the most made it to finals! Honestly they're evenly matched in my opinion so either outcome is alright with me so rather than focusing on one of them I think I will be comparing the two and letting people choose which they think is a more interesting way to haunt the narrative.
The injustice of his murder lies at the heart at all the following tragedies within the story.
His lack of agency within the narrative explores the effects of revisionism. There's so much we don't know about him or what he did during his life because his story is told by his murderer and by speculating historians.
Whilst his absence and the injustice of his demise haunts the story somewhat tangibly/directly there's most notably a counterforce that haunts the narrative coming from the actual Caleb. He created Flapjack who still shares his ambitions (to love and protect those dear to them) and who lovingly watches over and protects not just Hunter but his friends and families as well. His love for the Demon Realm is reflected all throughout the story in very small or subtle ways and its his descendants, literal and adoptive, who finally get their justice in the end. He represents everything that Belos was fighting the whole time, despite just being a ghost at this point, and that's what makes his way of haunting the narrative unique.
In pacifist and neutral routes, Chara's death similarly kickstart everything that happens thereafter but this is more directly because of their actions and decisions, their death being a lot more complicated. Their family is still alive to give you bits and pieces of their story and you see the way grieving them has shattered not just their family but also the entire underground. Their absence, what isn't known about them or their motivations, haunts just as much as their presence did.
What makes these routes unique for Chara is if you believe that the 2nd person narration in Undertale is told from their point of view and that they reside within Frisk to some capacity (a theory I adore personally and accept as canon even if it technically isn't.) There's something so beautifully haunting about being guided through the underground, their old home that they loved so much they'd die for it, by simple narration. Little things about their emotions and opinions show through once in a while, they quietly foster a relationship with Frisk and pass on their determination.
In genocide route, honestly I think it's less that Chara haunts the narrative but that you, the player haunt Chara by creating their narrative for them. They too have a lack of agency but in this case it's literal, they're a video game character, they cannot control their actions until the game allows them to defy you. Aftwards they stop haunting a narrative and start haunting you specifically. It's an exploration of RPGs from the perspective of the player character, it goes beyond having a narrative and being a direct communication between you as the player and Chara as your vessel.
What the choice boils down to
Assuming you're not just picking your favorite out of the two (which would be completely fair to do) and want to pick who you feel haunts their narrative more affectively the decision boils down to
Do you think the win belongs to a traditional but masterful take on a narrative haunter or to something that, while sometimes technically falling outside of what's normally considered narrative haunting, takes advantage of its medium and explores something new. Either decision is valid and they're both worthy.