WARNING: The following contains spoilers from the Dragon Ball Super manga, by Akira Toriyama, Toyotarou, Caleb Cook and Brandon Bovia, now available in English through Viz Media.
The Dragon Ball Super manga has settled into a comfortable rhythm lately as Goku and Vegeta regularly halt their training in order to go face a new threat. They've become all but official teammates, and low-key best friends, giving fans everything they've ever wanted for the two. This is why now is the perfect time to throw a wrench into things by pitting the mighty duo against one another.
Goku and Vegeta have not had a serious fight since the Buu Saga of Dragon Ball Z, and even then Goku was holding back. The two warriors have come a long way since then. Vegeta is now learning the ways of Destruction, while Goku continues to pursue Ultra Instinct. As they continue their quests into the domain of the gods, the question of who is stronger looms larger than ever.
If Goku and Vegeta simply decided to fight for the sole purpose of seeing who is stronger it would be quite a spectacle, but nothing more. Now that they've developed an almost brotherly bond, they stand shoulder-to-shoulder against every foe when it comes time to save the world. It's time for Dragon Ball Super to introduce a new conflict that finds them with strongly opposing views regarding the solution.
Vegeta most likely would not have a problem beating the great Kakarot into unconsciousness to get what he wants. However, it would be a great change to see Goku fighting for something other than the sake of fighting. A vicious, knock-down brawl over conflicting agendas would carry intense emotional weight behind it. After all, Saiyans only know one way to solve problems.
This theoretical conflict would almost certainly not be a clear-cut case of Goku is right and the Prince is wrong. During the Moro Arc, Vegeta expressed great regret for his past treatment of Namekians and took it upon himself to protect them from further harm. Capable of fighting for something other than himself, pitting his ideals against Goku would add a new layer to their relationship.
Conflicts in the Dragon Ball franchise are always pretty black and white: "this person is bad, let's punch them." It would be a fantastic conversation starter for the fans, debating which hero is right regardless of who ultimately wins. Goku and Vegeta are very different people, and just because they each fight on the side of right doesn't mean they're always going to agree on the best course of action.
This kind of conflict could even be taken a step further and force fellow Z-Warriors to choose sides for a full-on civil war in the Dragon Ball universe. Characters who have fallen to the wayside in the insane power-scaling of Super would have a better reason to enter the story than simple henchmen cleanup. A serious battle between allies that someone must win would be endlessly entertaining, more so than any martial arts tournament.
Emotional stakes are rare when everyone is either evil, good, or indifferent. Throw in the Dragon Balls to fix up any casualties or destruction and the stakes will always feel pretty low. Goku and Vegeta being forced to come to blows over conflicting ideologies would be a much-needed change of pace. A story is much more compelling when it is character-driven, rather than explosion-driven.