One of Star Wars' most interesting characters, Darth Plagueis, never appeared in the Skywalker Saga - but context offered by his apprentice Darth Sidious allows for an interesting comparison between the two Sith Lords. Throughout the Skywalker Saga, the galaxy was under constant threat from the machinations of Emperor Sheev Palpatine. As much as the Star Wars movies follow the Skywalker family, they also follow Palpatine's rise to power and eventual demise, with the Sith Lord acting as one of the major narrative threads consistently connecting the movies of the Saga.
The main story of the Star Wars prequel trilogy concerns Palpatine's rise to power as he establishes the Galactic Empire. He achieves this by manipulating the politics of the Republic and the Galactic Senate by facilitating war and consolidating his power, making specific use of his dual persona as both Sheev Palpatine and Darth Sidious to establish himself as the galaxy's Emperor. The Skywalker Saga doesn't delve too deeply into Palpatine's past, but he does refer to his own former Sith Master while tempting Anakin Skywalker with the dark side of the Force, and it's from this scene that much of the information about his history can be gleaned.
Though Palpatine doesn't reveal his personal stake in the story of Darth Plagueis on-screen, it has since been confirmed that Plagueis was Sidious' Master. As Palpatine's knowledge of the dark side of the Force is what tempts Anakin to join the Sith and become Darth Vader, the power of Darth Sidious is a key element of the Skywalker Saga's story. The power of Darth Plagueis is only hinted at through Palpatine's own story, but enough has been established about Sidious' former Master to suggest that he may indeed have had the upper hand. Though the answer is largely speculative, it hinges on some of Star Wars' most ambiguous plot threads.
What We Know About Darth Plagueis' Powers
Much of what Star Wars has canonically revealed about Darth Plagueis' powers has come through the context of Palpatine's own experiences and powers. Plagueis is described as a particularly powerful and intelligent Force-sensitive who trained extensively in the dark side of the Force and became obsessed with unlocking the secret to immortality. It's said that Plagueis eventually achieved the ability by influencing midi-chlorians to create life, leading to a manner of cheating death. It's also established that before Darth Plagueis died, he discovered the means of transferring his consciousness into other bodies using the Force, offering another sort of immortality. As well as these powers, it's implied that many of Darth Sidious' powers were also possessed by his former Master, as Palpatine studied the dark side alongside Plagueis as his apprentice. Palpatine also refers to Plagueis as a "prophet", hinting that he may have possessed some power of foresight or the ability to use the Force to glimpse the future.
How Emperor Palpatine Killed Darth Plagueis
As the story of how Palpatine killed Darth Plagueis is used in Revenge of the Sith as a means of manipulating Anakin Skywalker, it's relatively simple to surmise exactly what happened between the Sith Lords. Revenge of the Sith reveals that after believing he had learned all he could form his master, Palpatine killed Darth Plagueis while he slept, something that was made possible by Plagueis' growing obsession with immortality. Plagueis is said to have become increasingly paranoid about the Force striking back at him for his manipulation of the midi-chlorians, but ultimately it was his trust in his apprentice that led to his demise. Palpatine notes the irony in his Master's death, that his discovery of immortality indirectly led to his downfall.
How Powerful Palpatine Is Compared To Plagueis
Though Palpatine murdering Darth Plagueis seemingly indicates that the apprentice was the more powerful of the two Sith, this may not be the case at all. In many ways, it's difficult to surmise which of the two was more powerful simply because Plagueis isn't explored in the same way that Palpatine is. However, minor elements of Sidious' character betray the extent of his power, and it's hinted that in the end, it was his underestimation of his Master that led to Palpatine's death in Star Wars, which means that perhaps Plagueis truly was more powerful all along.
The manner in which Palpatine killed his Master is interesting, and perhaps evidences how powerful Plagueis was when alive. Sneaking up on Plagueis and killing him in his sleep was particularly interesting, as Sidious would almost certainly have had opportunities to do so while his Master was awake. This hints that Sidious was fearful enough of Plagueis' ability to wield the Force to carry out his plan while his Master was most vulnerable. What's more, Sidious reveals in Star Wars: The Rise of Skywalker that he believes Plagueis held back key knowledge of immortality, dooming his apprentice from beyond the grave. These factors combined seemingly indicate that Star Wars' Darth Plagueis was more powerful than Palpatine, although the latter's ability to manipulate others gave him a significant edge over his Sith Master.