I hate abstract theoretical arguments. And that's the only kind of argument that can reasonably be made in a battle like this. First off, are GT characters in this battle? saying DB universe is a little vague. Whatever, I'll just make arguments for both separately.
DBZ argument: Super Buu nearly destroyed the cosmos, as stated by Old Kai, it would have happened if not for Vegito. Even base form Vegito was curbstomping Super Buu. And by the end of Z, Goku gets at least 400 times stronger. So I would say Super Saiyan Vegito can easily wipe out the entire cosmos, (in other words, existence itself) what would happen after existence is wiped out? Who knows, hence the abstract part. Could Tenchi survive existence not existing? How about Vegito?
It's difficult to even think of a battle like this in terms that would be remotely correct, as the concept of omnipotence and reality without existence is a little beyond the ken of Humans and our limited understanding of the universe.
DBGT argument: Goku appears to have some level of omnipotence after absorbing 6 of the 7 Dragon Balls. Based on his appearances 100 years later, it's safe to say he's transcended death in some way. End of GT is certainly getting past Super Buu levels of power for unfused characters, so theoretically Goku could probably destroy the cosmos as easily as Vegito, if not more so. Since the fusion earrings are x*y instead of x+y like the fusion dance, if end of GT Goku fused with end of GT Vegeta and made SS4 Vegito post Dragon Ball absorption, I believe that would certainly cross over into omnipotence, if Goku wasn't there already. The universe was after all made by someone with a power level of only 120 billion. :)
Either way, putting omnipotence vs omnipotence or omnipotence vs infinite destruction, is unquantifiable and undefined. It's like a mathematically equation where you end up with something like 2=5, it's an inconsistent independent system.
Personal opinion: The following is my personal opinion, not an argument. I don't believe omnipotence exists. I think things can become so powerful that ordinary people would think of them as omnipotent, but I believe a big enough hit will kill anything. When I decide for myself which "omnipotent" would win in a fight, I like to base it on actual showings, bonus points if said character used to not be "omnipotent" as that way you can see a progression of the character's power. Basically, I like to think of it in terms of a giant number line. I believe when it gets to a certain point, most people would just label it as (x,∞), when in fact it should just go to an extremely high number, not infinity. In the case of Goku, (I'm not going to comment on Tenchi specifically, since I don't know his pre omnipotent feats) I believe his ability to destroy was already at an omnipotent level at the end of Z. 400 Times stronger than Kid Buu puts him at least equal to Super Buu in my mind. So getting stronger than that, is essentially an infinity+ level to me. And I believe that Goku, (or Gogeta/Vegito if you wish, though of course they're just Goku with stuff added on) is more powerful than any character that doesn't show the same kind of multiplicative scaling that he does, past "omnipotence".
Disclaimer: I'm not going to take arguing in this thread super seriously, as I believe there's little point, and I doubt I will convince many, if any people of my point of view. There's not many places for an argument like this to go really, I've tried them before. They always end up as philosophical discussions of the unquantifiable, which is fun in a limited sense, but not something I enjoy extended vigorous back and forth on.
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