Gohan would work better thematically due to their connection, with Gohan being forced to use SS2 and the rage Gohan feels towards Babidi allows him to tap into his previous peak. Vegeta and Goku choose not to intervene because of their pride, though once seeing how close Boo is to reviving, they kill Dabura and attempt to stop Boo's revival. When that fails and they see how strong Boo is, Goku uses Shunkan Ido to teleport Vegeta away to the Heavenly Realm. Piccolo soon comes to his senses and he and Gohan follow.
Goku then teaches the Saiyans Fusion in the time he has left, with Gohan and Vegeta eventually mastering it enough to fuse and face Boo. With their fused power as a Super Saiyan, they easily kill Boo before dealing with Babidi and peace is restored.
For Super, the main events go the same for the most part. Beerus simply inquires about Super Saiyan God after the party and Goku tells everyone via Kaio it may be best to revive him after they use the Dragon Balls to find out about it. Things then go the same until the U6 tournament, which has two changes. First, Gohan would replace Boo. For the sake of the plot, I'll say he gets as much of a plot boost as anyone in Super and ends up slightly below Goku and Vegeta in the same form through training with Piccolo. Secondly, Piccolo would be a fair bit stronger than in canon due to starting off at a higher level due to the Majin boost prior. I'd say in this scenario, he's able to equal Frost's power and defeat him through wearing him out, though it costs enough that he's unable to handle Magetta. I'd say Gohan would go first against Botamo and face the same fate as Goku against Frost, though would be brought back into the tournament once Piccolo lost. He beats Magetta by going SS2 and then faces Cabba. Whilst tutoring him like Vegeta did, Gohan's soft nature prevents Cabba from going Super Saiyan and, thus, he is defeated. Gohan quickly loses to Hit and whilst Vegeta fares far better with SSB at 100%, he is ultimately defeated due the stamina issues and still being unprepared for Hit's Time Skip. Goku's preparedness and Hit's fatigue would allow Goku to defeat him though.
Future Trunks Arc goes the same. For the ToP, Gohan and Piccolo end up somewhat stronger than in canon, though not by much greater than their peaks. Another noticeable change, however, would be that U6 would lack Super Saiyans beyond Kale under the right circumstances which would mean even if Kefla happened, she'd be far weaker than in the manga. Hell, Freeza or Dyspo would probably beat Caulifla before it happened. That said, Gohan lasts far longer (though Piccolo is still taken out with a sneak attack, even if probably gaining more victories) and is able to help out somewhat against Jiren before inevitably losing.
Only other change is that for the Broly Arc, Goku and Vegeta don't need as much time, if any, to master using the fusion dance.