I found DBO's decision to have them both realise their impending natural death and choosing to die whilst settling their rivalry was a good end to their character arc. Before that, I'd gradually build up their acceptance of their finite lifespans being a heavily emphasised reasoning as to Oob's training, moreso than the bland desire to fight someone strong.
As for how it would go for Super specifically, Vegeta could remain virtually the same in regard to how family has become his driving force, minus his poorly handled rage boosts and his regression throughout the ToP. Goku, on the other hand, is quite hard to figure out. His desire seemed to be to retire in the Boo Arc and would have had the plot not dragged him back into the spotlight. This should have been the focus in Super as even if he were to achieve the God forms and seek further strength, he should've spent at least equal time tutoring Gohan and Goten on the importance of getting stronger and protecting the Earth after he's gone.
