Let’s point out the obvious and state that Darth Vader would never face Palpatine in his prime since the days when the Emperor could swing a lightsaber with the best of them were long gone by the time Return of the Jedi had come around. The use of the dark side of the Force had warped Palpatine in such a way that getting around was difficult enough, but trying to duel with someone like Vader would have taken a serious amount of strength, both physically and in the Force. That doesn’t mean that it would be an easy fight, not in the least. The Emperor has a couple of weapons that his apprentice can’t access, and because of this, it’s fair to say that Vader might not be able to wade through his master as easily as some might think. But the battle that would take place between these two would be all kinds of awesome since the implications are far-reaching and would have, had it happened, changed the Star Wars franchise in a very big way. If nothing else, it would have been a grand battle to watch.
One has to remember that as eager as Palpatine was to enlist Anakin Skywalker into his service, or rather, ensnare him as many would put it, he was also bound to torture his apprentice more than once during their time together. He did the same thing to Darth Maul throughout his apprenticeship. While each person is different and replies to various stimuli in different ways, Palpatine was never hesitant in showing his apprentices their place. More than once he reminded Darth Vader of where he stood and why. Yet for all that, the apprentices continued to follow the Emperor, and for reasons that were explained but also hard to understand since hatred and the lust for power tended to war with each other until each apprentice believed that they could take Palpatine on and eliminate him.
It was even stated that the Emperor had foreseen this, and was well aware that his apprentice would attempt. And yet, nothing ever came of it for many reasons that were usually hidden away. This fight would have been amazing, to say the least since if Vader had recalled that Force lightning could be caught on the blade of his lightsaber. Amazingly, this wasn’t a part of the original trilogy, though it’s fair to see how no one would think of it when the scope of the movie was so large that trying to keep everything in perspective was already a daunting task. But while the Force lightning might be negated in at least some way, it stands to reason that Palpatine’s devious nature and his knowledge of Anakin’s past would afford him another few weapons that would allow him to gain an edge on the masked Sith. The techniques that Palpatine used against the four Jedi Masters that came to arrest him in Revenge of the Sith would be an interesting quality to try and use on Vader, but there are not a lot of guarantees that it would work. For one thing, Vader is well aware of what his master can do, at least in part. So thinking that the manifestation of such a power would be quite as possible, in theory at least.
Those who think that Sidious would prevail aren’t entirely wrong, since his mastery of the dark side of the Force is impressive, to say the least. But one also has to remember that Vader’s anger is often a destructive force all on its own. While Vader isn’t quite like the Hulk, he doesn’t get stronger when he’s angry, he can tap into a few very impressive reserves of strength when someone triggers a particularly painful memory. In this manner, he’s able to dig deeper and produce a far more pronounced effect than when he’s simply reacting to a threat. Apparently, George Lucas has even stated that Vader in his prime is only about 80% as powerful as Palpatine, and as everyone knows, what Lucas has said in the past has been seen as gospel when it comes to Star Wars since he created the franchise. But at this point, it’s fair to say that a lot of fans are willing to disagree with the creator as the desire to see Vader as a legendary character that can beat just about anyone has been well noted.
In the end, this fight would come down to the barest slip by either Sith Lord since the two are incredibly powerful and have their own strengths and weaknesses that would be exploited throughout the fight. To predict a winner would be to invite an argument from either side, those that favor Palpatine and those who follow Vader. Either way, no matter who won, the galaxy would still be in a world of trouble.