It's a part of Anakin's past that Vader wants to get rid of, but can't at least in the physical sense. From Palpatine perspective, Vader has spent enough time and energy on Obi-Wan and couldn't bring a conclusion to it, so he doesn't want Vader to waste anymore time on it.
So instead of risking letting his emotions get the better of him, Darth Vader opts to let Obi-Wan go with the assumption that he is no threat to him or the Empire.
Seeing Anakin as Darth Vader understandably breaks Obi-Wan's heart. He couldn't bring himself to kill Darth Vader, however, because he continues to associate him with the Anakin he trained as a boy.
Admiral Ozzel : [appearing onscreen with Captain Piett] Lord Vader, the fleet has moved out of lightspeed and we're preparing to... Darth Vader : You have failed me for the last time, Admiral! Captain Piett?
In that time Anakin apologizes to Obi-Wan, desperately asking him to forgive him for everything he has done to him and everybody over the years. Obi-Wan's response was teaching Anakin how to do connect with the force and keep his spirit intact.
Darth Vader hates Obi-Wan, not because he blames him for his fall to the Dark Side, but because he turned Padmé against him and destroyed his body. The line from Obi-Wan Kenobi, "I am what you made me" isn't a reference to Vader's fall to the dark side.
During the Imperial Era, a human female nurse served the Galactic Empire on board the Death Star under the supervision of a doctor. They both served the Sith Lord Darth Vader as his personal medical caretakers. The nurse became obsessed and psychotically in love with the Dark Lord of the Sith.
Obi-Wan also let Vader go because Vader wanted his old master to kill him. Sometimes being left alive is more of a punishment than death. But now Obi-Wan could walk away knowing there was no hope for saving Anakin — until Luke finds a way.
During Mandalore's Civil War and his apprenticeship under Qui-Gon Jinn, Obi-Wan fell in love with the young Duchess Satine Kryze. The two lived on the run for over a year.
1/15 Luke Skywalker
Having faced his father once before, Luke was familiar with his tactics and used the force to gain an upper-hand. In Star Wars Canon, only Luke Skywalker can be acknowledged as the one who truly defeated Darth Vader.
As soon as Anakin Skywalker became Darth Vader, he already faced his most persistent nemesis and lost, namely his own master, Obi-Wan Kenobi.
The short answer is yes, without a doubt, Vader regretted becoming a cybernetic monstrosity. First, there's the constant pain and discomfort from his suit. Worse, however, is the psychological pain. Vader destroyed everything he had ever known for a chance to save Padme.
Between Darth Vader and Obi-Wan, it's pretty clear that Vader is far more powerful with the force. After all, he pretty easily used the force to stop a starship from taking off in the previous episode, and manhandled Kenobi throughout the majority of the show.
His armor could be hacked and controlled by a device. In a turn of events, Darth Vader's right limb holding his dangerous scarlet lightsaber was moving of its own accord toward his neck. This was a dangerous weakness indeed.
In a Vanity Fair interview from 2005, George Lucas went deeper into why Anakin became much weaker as Vader. In the interview, he explained that because Anakin's limbs were severed and replaced by robotics, it was harder for him to use the Force than it was before his battle with Obi-Wan.
Did Darth Vader ever lost a fight? Darth Vader is one of the greatest villains of all time. But even he gets beaten sometimes. CBR lists all of the folks who managed this improbable feat!
The ever stronger fear
In the Phantom Menace, Master Yoda senses much fear in Anakin, however, this fear is not the understandable anxiety - Anakin is afraid to lose his mother, Shmi, whom he was forced to leave behind in slavery.
Although his choice to help with the droid attack on the Wookiees seemed to be a prudent one in Star Wars: Episode III - Revenge of the Sith, Yoda's Kashyyyk mission was actually his worst mistake.
Fighting Emperor Palpatine
Though Yoda was able to keep his adversary on his toes, he was unable to end the conflict, and their duel ended with no clear victor.
The Third Sister Was a Jedi Youngling
The reason why the Third Sister hates Obi-Wan Kenobi so much is because she was a Jedi initiate when Order 66 happened. On that infamous day, Reva was training with her fellow Jedi younglings in the Jedi Temple of Coruscant.
Obi-Wan Kenobi's most powerful villains in Star Wars include his greatest enemy Darth Vader and less well-known ones like Darth Krayt.