Yoda chose to retreat as Sidious cackled in triumph above him. If the galaxy had any hope of freedom from the Sith, Yoda realized that he needed to survive for that to happen.
While on the floor of the Senate, looking up at the cackling Emperor above him, Yoda clearly realized that he couldn't beat Palpatine in one-on-one combat. As considerable as his own power in the Force was, Palpatine's at that moment was even greater, and to continue fighting would likely only result in his demise.
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.
Yoda fled because he believed he would lose, and his life was more valuable than to be thrown away so carelessly. Yoda won the long game, but absolutely, definitively lost the short game. In terms of the battle we are presented, Sidious was the victor.
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.
Yoda and Palpatine once engaged in a skirmish on Coruscant during the events of Star Wars: Revenge of the Sith, until the evenly matched duel ended in Yoda retreating. Palpatine proved in that confrontation that, with his use of the dark side, he was able to best the Jedi Grand Master.
Palpatine was more focused on building the Galactic Empire. While his apprentice was wasting precious time and resources by hunting down an already defeated enemy. I'm surprised Darth Vader's obsession didn't get him killed.
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.
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.
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.
Yoda's presence on Dagobah was likely hidden due to his mastery of Force Stealth and the planet's connection to the Force. Yoda, with his enhanced Force abilities and potential home-field advantage, would have had the upper hand against Darth Vader if they engaged in a lightsaber duel.
Windu has created and fully mastered Vaapad, a variant of Form VII. Yoda mastered the original variant known as Juyo. Both of them were able to fight with Palpatine on equal ground, matching him blow for blow. It is stated that Yoda beat Mace in a sparring match.
Even though Sidious mastered all forms of lightsaber fighting, Yoda can smash anybody (besides Luke in episode 7) in a lightsaber battle. Brute strength: Palpatine takes it. Palpatine can lash out with the force and do more damage than Yoda in one lightning bolt. Control: Yoda is the clear winner.
Palpatine used his powers to hide his true nature from the Jedi, utilizing Force Concealment to completely hide his presence in the Force while clouding the Force for the Jedi. The Clone Wars also kept the Jedi busy and weakened, preventing them from realizing his true identity.
Even if Yoda did not want to arrest Palpatine, with Mace there, the two could have killed Sidious before Anakin could stop it, given that Anakin only arrived on the scene moments before Mace had the chance to slice through him with his lightsaber.
It became seen as a gateway to the dark side, with some choosing to practice it in secret. Remarkably, Mace Windu is only one of a few Form VII users who didn't fall to the dark side thanks to his refining Juyo into Vaapad.
