Yoda declared that Sidious' reign was over and not a moment too soon. Not wanting to take any risks at his moment of triumph, Sidious attempted to flee but Yoda blocked his way, igniting his lightsaber.
Moreover, throughout the duel, Yoda continually adapts to and even matches Palpatine - forcing his enemy to constantly attempt new tactics. Palpatine clearly hated Master Yoda with a fierce passion, but he was under no illusions that the Grand Master would be easy to defeat.
Sidious concealed his nature. Yoda sensed that the Dark Side was focused on the Jedi Order, but he didn't recognize Sidious until it was too late. The clearest demonstration of Sidious's skill is the fact that he dealt in person with Jedi Masters for 20 years and they never realized what he was.
Palpatine both feared and respected Yoda, with some faint contempt. Yoda held his ground whilst battling Palpatine at the Senate building and demonstrated that he could match the Sith Lord in raw power, even if he did fail in defeating Sidious.
Master Yoda knew that Darth Vader was once Anakin Skywalker - the boy he sensed too much fear in to train way back in Star Wars: Episode I - The Phantom Menace. For many years it's been assumed Master Yoda was aware from the day Vader gained his cybernetic enhancements and signature wheeze.
Why Yoda Never Looked For Mace Windu's Body - Star Wars Explained
Why does Darth Sidious not like lightsabers?
He believed that the Sith, who had used lightsabers for tradition since the time of Darth Bane, should have moved on from using lightsabers (which, though invented by a Sith, had become the symbol of the Jedi) and instead rely entirely on scheming and the Dark Side of the Force to earn and maintain their power.
As Palpatine's apprentice, Darth Vader was well aware of his Master's true identity; indeed, the revelation that Palpatine was Sidious was instrumental in Anakin Skywalker's fall to the dark side in Star Wars: Episode III - Revenge of the Sith.
His connection to the Light Side was too strong, and indeed, his willingness to follow it over the dictates of the Council made him far more dangerous to Darth Sidious' plans.
Yoda had to shoulder that decision for years. However, he ultimately understood the importance of life, and the power he could have used to defeat Dooku would have been much better used to preserve two lives. Over the years, Dooku would commit countless atrocities and also suffer incredibly embarrassing defeats.
Dooku could have not beaten Yoda in Geonosis, meaning that the fight would have ended with Dooku either killed or captured had it continued. At that point, the only two Force-sensitive warriors who could beat Yoda in a fight were Mace Windu and Darth Sidious.
Dooku belonged to the aristocracy, and his weapon reflected an older, more chivalric style than the Jedi he faced. It also reflected his status as the head of the Separatists: the lightsaber looked far more ceremonial than practical, suggesting that he himself did not face combat nearly as much as the Jedi did.
As Darth Vader, he was one of the strongest beings in the entire galaxy. But even then, he was never able to surpass his master, Darth Sidious. A Sith Apprentice can only become the master when they murder the one who trained them.
R2-D2 was present when Padmé gave birth to Leia and Luke, so he knew Luke was Anakin's son – but what he didn't know was that Anakin became Darth Vader. In addition to that, Anakin's fall was surely a painful event in R2-D2's life, one that he definitely wouldn't like to remember or even talk about.
Over the years, Anakin came to highly respect Yoda, while Yoda gradually outgrew his fear of Anakin and came to have faith in him and correctly came to believe that Anakin was the Chosen One from the Jedi prophecy.
Summary. Palpatine's true source of power comes from his intense hatred for everyone in the galaxy, which only fuels his strength. Not only that, but the more people hate Palpatine, the stronger he becomes as well, making inspiring hatred a crucial part of increasing his strength.
We are just barely seeing a 600-something-year-old Yoda in the High Republic era. And given that Qui-Gon Jinn dies in 32 BBY, a fight beyond that point would be pointless since, as a Jedi spirit, Jinn would arguably be stronger than the still physically alive Yoda.
Palpatine was disappointed in Vader. That is, until he sensed Vader was trying to use his son Luke to aid him in taking him down at last. He envisioned three outcomes: One, that Luke would slay Vader and embrace Palpatine as his master. Two, that Vader would slay Luke and prove himself to be the worthy successor.
