He suspected that interacting longer with Obi-Wan could still bring back Anakin Skywalker, which would very likely spell the end of his reign and the Galactic Empire.
Given his pent-up anger and power level, the Sith Lord could have easily ended the Jedi quickly. Instead, after burning him on the ground, he allows him to escape — an interesting decision but a sensible one given the villain's ultimate plan. Darth Vader doesn't want Obi-Wan to die instantly; he wants him to suffer.
Vader doesn't regret falling to the Dark Side (Anakin does). He regrets being defeated by Obi-Wan. That's why, when he sees that Obi-Wan is full of guilt, and no longer wants to kill him, he "comforts" him by saying that he's not his failure.
Deborah didn't want that theme playing every time you see Darth Vader, she wanted to explore his journey to get there. Indeed, there was a desire not to lean too heavily on the original songs and instead be much more nuanced about adding them in ways that connected to and enhanced the story.
In contrast, Vader was able to sense his personal connection to Luke Skywalker almost immediately. This raises a question as to how he could detect his relationship with one character but not the other. The short answer is that creator George Lucas had no idea Leia would end up becoming Darth Vader's daughter.
In order to hide from the Empire, he needed to keep a low profile. This means that he's not in his best fighting form. Couple that with his wavering faith and he isn't really attuned with the Force, further impeding his fighting skills.
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.
Obi-Wan knew it was only a matter of time. So, he made the difficult decision to use his learnings and become one with the force, rather than let Vader decapitate him.
Vader believed that his and Padmé's child died when she did, so there was no reason for him to consider anything else.
All in all, Anakin felt incredibly betrayed by two of the most important people in his life. We all know he has quite the abandonment issues, and the fact that Obi-Wan and Padmé leave him is likely the primary cause of his extreme hatred.
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?
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence.
Because he was not an active member of the Jedi Order during Order 66, Infil'a escaped execution. Some time later, he faced the Sith Lord Darth Vader wielding a green lightsaber. Infil'a put up a fierce fight against Vader, almost killing him by throwing the Sith Lord off of a cliff.
Vader held respect for Tarkin which is clearly shown and the only case in which Tarkin outranked Vader would be the case in which Vader was in the Death Star or within Tarkin's Oversector which he likely was as Tarkin was Grand Moff of the Outer Rim Oversector, the largest one.
Darth Sidious
In the end, Vader managed to fulfill the prophecy tied to him. As for Darth Sidious, he's by far the most dangerous enemy Vader has had. Becoming emperor of the galaxy and crushing most of the Jedi was proof enough.
Anakin may have a tendency to disrupt the equilibrium of the Force, but he still has the ability to save himself. However, as he becomes more and more consumed by the fear of losing those he is closest to, Anakin loses the balance and is consumed by the Dark.
Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master. Obi-Wan assures Anakin that he is proud of him, telling him that he has become a "far greater Jedi than I could ever hope to be."
Short answer? No. It's been clear that the main issue had to do with Anakin's mental state. If Anakin just got the help he needed and stayed loyal to the Jedi Order, overcoming Palpatine's evil temptations, Padmé would've survived.
In Star Wars Legends and Canon, Galen Marek (Starkiller) is the only Jedi (other than Obi-Wan Kenobi) to put a beat down on Darth Vader/Anakin Skywalker. Galen was secretly trained as a Sith Lord apprentice to Vader, but returned to the light side and the Jedi.
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.