The ACTUAL argument
The thread I just posted a few hours ago was actually a troll thread, it was purposely poorly put together, just to see if anybody would take the bait, the results were not disappointing. This is the actual argument I have. It's much more well put together and written in my opinion, as well as the opinions of those who read it where I posted it the first time. I'm sharing this one as evidence that I can actually make a good argument and that I'm not actually a complete idiot, as some of you probably think.
I'll start by looking at their accolades, specifically those that state them as being the most powerful Sith Lord in history. Both of them have these accolades, and both of them have several of these accolades at that. The difference is that Viiate's are newer. A quote by Leland Chee would suggest that all newer content overwrites older sources and another one from him states that any source can be challenged if there is a notable contradiction in either another source, whether it be accolades or feats.
Now I'll look at their actual power. Sidious is stated as being an "event horizon" and a "black hole" in the Force, where-as Vitiate is stated as being a "god-like avatar of the Dark SIde" Vitiate is also powerful enough that he is actually a Sith entity, meaning he doesn't need to have a physical form to retain most of his power. Darth Marr was actually afraid of how powerful Vitiate could become without a corporeal vessel. In "Rise of the Emperor", Vitiate was able consume the population of Ziost with no rituals, just a full powered drain. While it's true that Sidious was able to hide himself from right under the nose of the Jedi, which is incredibly impressive, it's also known that several other, far less powerful Sith, were able to do so as well; such as Darth Zannah and (more impressively) Baral Ovair, who hid his presence as a Sith agent for decades. Vitiate himself hid from the Jedi for over a millenium, and the Jedi never got more than inkling of a though that something was wrong. Suggesting Vitiate's power to conceal himself is much greater than Sidious' own.
We can also look at their examples of planetary drain. Sidious was able to drain the population of Byss slowly to retain his power, but it required that he focused on doing so for all that time, implying that it wasn't easy for him to do. Vitiate's example of planetary drain, draining Ziost, was immediate, and not only killed and absorbed all sentient beings on the planet, it also left Ziost a barren wasteland. Another comparison of their actual power is this, Sidious is the greatest example of Banite scaling done right. He has more power behind him than any of the previous Banite Sith Lords, and considerably so at that. Hence his accolades of being an event horizon and a black hole and what have you. Vitiate, however, contains, at BASE (considering him post Nathema ritual as base) has the combined power of 8000 Sith Lords from Nathema, keep in mind that these were Sith alive during the golden age of the Sith, meaning they would have been powerful. He was so powerful that his mere presence on Dromund Kaas turned it into a stormy and dark planet, and he turned the planet into a Nexus of Dark Side energy by simply being there and performing other rituals. Let's also not forget that Luke Skywalker compared Sidious to Exar Kun, suggesting that even Exar Kun (who is canonically inferior to Vitiate) may be on par with at least ROTS Sidious.
So now, we know that lesser Sith have been capable of doing things that Sidious has done, on the exact same scale. And we know that Vitiate was able to do these things on a larger scale. We also know that Vitiate is an entity, which is a level of power that Sidious has never reached, or at least is never directly stated as having reached.
Now we look at their most impressive feats. Let's go right to the one everybody is going to bring up, Force Storms. Many Sidious advocates will use this argument to say that Sidious is more powerful than any other Sith Lord; I disagree. We know from Dark Empire that Sidious' Dark Side Acolytes, when they use their strength together, are capable of summoning these storms, and they're significantly weaker than Sidious is. We also know that Jedi Master Thon is credited with the ability to use these storms as well. This puts things into perspective, because now we know that Sidious isn't the only person that can use Force Storms, which makes Sidious' feat considerably less impressive now. Sidious is also stated as being believed to have learned all Dark Side powers in existence, with the ability to formulate new ones at will, this is also highly contestable. As the quote never actually direct says that "Sidious learned all power, the end" it says that he is BELIEVED to have done so, meaning that Sidious' mastery of every ability is really nothing more than a rumor and conjecture. Just as well, his supposed ability to create new powers on a whim is ludicrous s well, as Sidious never once demonstrates a power of his own creation like that. On the flip side of that, Vitiate is directly stated a having delved into the deepest and darkest aspects of the Force in his pursuit for immortality and power, mastering every ability he came across.
Vitiate, as a boy, was able to mentally dominate Lord Dramath and kill him at the age of 10, and at the age of 13 Vitiate had become powerful enough to gain the notice of Marka Ragnos, the most powerful Dark Lord to live up until that point in time. Sidious was certainly powerful as a child, but to easily dominate and kill a fully trained Sith Lord at age 10 is something we never seen from young Palpatine. We should also consider that Sidious, as the Emperor, was nearly killed on Korriban by the spirits of long dead Sith; Vitiate was the most powerful ancient Sith. If Sidious was incapable of dealing with the weakened spirits of unnamed Sith Lords, then why should he be able to defeat Vitiate, who is factually far more powerful than any of those ancient Sith? Let's also not forget that Vitiate easily defeated not one, but two of his Dark Councils that plotted against him. Destroying them, supposedly with ease.
Now let's look at them as spirits. This is honestly where Vitiate trumps Sidious without question. Vitiate is stated as being an entity, which as I said earlier, means he doesn't need to have a physical body to retain a large portion of his power. This is made quite evident by his draining of Ziost as a spirit, as well as his many feats in KOTFE and KOTET as a spirit, including ragdolling the Outlander, and incinerating Skytroopers with a wave of Dark Side energy, or using his weakened power to easily dispatch his son Arcann. The point being, Vitiate/Valkorion is still IMMENSELY powerful as a spirit. Sidious, on the other hand, is useless as a spirit. He can't do anything combative as a spirit aside from essence transfer. So if the two encountered each other as spirits, Vitiate/Valkorion would dominate him.