The topic post confuses me. The topic title says SSj3 Vegito, but the post says SSj2 Vegito. Which one is it?
Not that it matters, though, because in either case, the battle is very similar. To my knowledge, the rationale for Pre-Crisis Superman being Multi-Solar System level is having numerous extremely casual Solar System level feats. Even if he went full power, I imagine it would only push him to the realm of low 4-A at best. On the other hand, Vegito in any of his forms is vastly superior to Kid Buu who can eradicate galaxies in the span of only a few years. Vegito is thus likely high 4-A as opposed to Superman's low 4-A. See where this is going? The gap is big enough that I don't think Superman is going to be able to inflict any significant damage to Vegito initially. What makes this interesting, however, is that the same can be said of Superman. Apparently, he tanked the Big Bang, which would result in high Multi-Galaxy level durability at the very least. He also has an astronomical speed advantage. With those two factors, Vegito will have an even harder time harming Superman than Superman will have trying to damage him. Thus, the fight will stalemate initially as neither can seriously harm the other.
What tips this in Superman's favor is that he can outlast Vegito and break the stalemate through patience and cunning. Vegito has vast, but still ultimately limited reserves of ki, which can only be restored through rest and other mundane methods such as eating, which he has extremely limited access to in this fight. Superman's power comes from stars, of which there are countless in number across the universe. If Superman ever becomes tired, he can simply fly to a star and restore his energy or perhaps even boost himself by sun-dipping. Nor can Vegito ever deprive him of his power source as if Vegito ever destroys a star, Superman can simply fly to another one somewhere in the universe and recharge there, completely out of Vegito's reach since he is too fast for Vegito to pursue him. Meanwhile, Superman can deprive Vegito of rest or food by keeping a constant offensive. Eventually, Vegito's ki reserves will deplete, fatiguing him and leaving him drastically weakened, allowing Superman to finish him.