Prove me wrong. I'm a lore expert on Destiny, so odds are I can refute any argument you provide that favors Destiny. Vegeta and Goku would beat the entire Destiny universe in a fight.
Lets also assume they know the mechanics for the VoG and Crota's End.
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Well, Goku and Vegeta never played well together unless THEIR friends/planet/universe is in trouble, so I don't know about this. In Vault Of Glass Goku would be useless because all he knows to do is hit things. Plus you need more than 3 to finish at the end. One could argue Goku could use a Spirit Bomb before Atheon teleports them, but it takes time to gather and you need beings willing to give you energy to make it more powerful, so using beings from the Destiny universe would be out of the question if they are indeed fighting in the Destiny universe. Plus the fact that those with a pure heart, in this case the guardians fighting the darkness, can't be harmed by a Spirit Bomb. Crota would be another story, because Goku and Vegeta both trained with extra gravity, so the pit would be easy to finish. And the rest of the fight is basically "kill this, move on, kill this, repeat", so they'd finish it. On the Destiny universe side of things, we don't fully understand how the Darkness or Light works, so we don't even know if anything in this universe could harm Goku/Vegeta. My thought is that they wouldn't be able to harm each other because it would be Light vs. Light. Based on what Destiny has shown already, it seems only Darkness can conquer Light(Guardians), which neither Goku nor Vegeta is filled with or use(Meaning they don't fight using Darkness. Not light.) Plus the fact that Guardians can be endlessly brought back to life as long as there is light, whereas Goku/Vegeta can only be brought back by the Dragon Balls IF they aren't more powerful than the dragon himself. (The last time they tried to revieve Goku, I believe, the dragon said something along the lines of him being to powerful to be forced back to life by his powers.) Bottom Line: If they fight in each others universes, there are drawbacks on both sides and inconsistencies, too. Even if they fought in a different universe that wasn't Destiny OR DBZ, they would be at a stand still. Both universes are still expanding, too, so drawing a conclusion at this time wouldn't really be fair for either side.