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In the short where we see them on friendly term(more than friendly) they seem rather similar. Both snarky and classy. So what separates them is the circumstances where Jackson lost everything because his family sold everything, including their title, to try ending their debts... and it wasn't enough.

Our first instinct it to be on Prim's side. Jackson robbed her, his fiancée.

But she is not exactly... ideal.

During the tavern scene where Jackson tries to convince Prim to let him join the king's quest we see how little Prim gets him. Which makes sense, she assumes he is the same just more scumbag like. She thinks Jackson is ready to abandon his team because he thinks they are beneath him. That is not exactly it though. Jackson is ready to abandon them but he does feel scummy about it. He wants to ditch them because he is tired of being an adventurer, that he wants a nice lifestyle again. He is selfish, but he is also sure his friends will be fine without him.

And Prim shows her greatest flaw: She overplays her hand. Like Jackson points out later, she is not ready to just take a win, she is convinced she got everything under control and keeps betting when she shouldn't bet. So she insults the other adventures Jackson is traveling with. She does so because she assumes their company is what bothers him because ten years ago it would. Because they are beneath a noble, even one who lost everything he had. But instead of insulting Jackson for his lack of dignity, she just insults his friends. Especially Pepper who is more or less his little sister. So Jackson withdraws his offer and even makes a snarky remark. And Prim doesn't get it, she just thinks it is because she hurt his pride.

Worse is when the dragon is going crazy. Jackson offers his help, he even gives her the necklace back to show that there is no catch, he actually feels bad about robbing her specifically and just wants to stop the dragon... And she makes a big deal out of not needing him or his "lowly" team.

She is the protector of the regon... which is just a fancy way of saying glorified city guard. She should be thinking of the town's best interest and accept Jackson's help. But she overplays her hand, refusing his help just so she can have the satisfaction of not needing him.

YES, Jackson and co. runs away like scumbags, not very heroic. But he DID offer to help... and then left when she said no, that is kinda petty. But we should also keep in mind that Jackson hates the town, that something happened that resulted in his family losing everything and Jackson was (according to what we can gather from his short) laughed at and shut out of high society. He is not very heroic but we can get if he is not overly ecstatic about trying to save a place he hates with a burning passion.

So... Jackson is kinda scummy and is acting on self interest. But at the end of the day, he value his group's safety and happiness. He is tempted to ditch them but sticks with them. He is not that bad of a guy. Prim however is more interested in image and not only doesn't have her own town's interest first, she is putting her team in danger by not accepting Jackson's help out of spite.