Phantom, the adopted son of Frostbite, heir to Far Frozen, and Robin, the adopted son of Pandora, heir to the Acropolis of Athens, hated each other to death.
It could be due to their opposing cores, with Phantom being an ice core ghost and Robin being a fire core ghost. Or because of how much they were compared to each other in the Realms, since they had both appeared at the same time.
Their haunts had also lined up next to each other, which didn't help the ghosts' constant argument over "Who's better?". They also had similar abilities, and their outfits looked "heroic" which amused the ghosts a bit. When two Ancients adopted them and proclaimed them heirs, the argument only escalated.
Strangely, none of this was the reason they didn't get along, their mutual hatred stemmed from being too similar. Their personalities constantly clashed but there was a big difference.
While Phantom went through the Fenton portal and played a hero in his dimension constantly, Robin was afraid of the portal, his previous dimension did not bring back good memories so he guarded Acropolis and stayed away from the realm of the living.
Jason hated Danny, but that wasn't exactly right. Jason hated that Danny played the hero, that he took responsibility for his parents mistakes like it was his duty, that he came back with constant injuries and a smile on his face but then hid in his haunt and cried at night. He couldn't understand it.
Jason was a hero, and he was tired of it. Danny hated that Jason held back, that he would give up on his connections, he couldn't imagine himself abandoning Sam, Tucker or Jazz. They had taken different routes and neither of them could understand it.