"Anakin, as Skywalker, as a human being, was going to be extremely powerful,” he says. "But he ended up losing his legs and an arm and became partly a robot. So a lot of his ability to use the Force, a lot of his powers, are curbed at this point, because, as a living form, there’s not that much of him left. So his ability to be twice as good as the Emperor disappeared, and now he’s maybe 20 percent less than him. So that isn’t what the Emperor had in mind. He wanted this really super guy, but that got derailed by Obi-Wan. So he finds that, with Luke, he can get a more primo version if he can turn Luke to the Dark Side. You’ll see, as this goes on, Luke is faced with the same issues and practically the same scenes that Anakin is faced with. Anakin says yes and Luke says no."
- George Lucas, "The Last Battle", Vanity Fair
My answer here lays out quite a bit of evidence from the original scripts and a now noncanonical materials that expose the mutual animosity between Palpatine and Vader. Much of Palpatine's dislike for Vader stems from his disappointment at Vader's limitations due to these unforeseen injuries.
Even as he made his way to the body, Sidious wrestled with anger and indecision. Part of him wanted to leave what was left of Vader to burn to ashes in the rising lava for his failure. As he walked however, he reasoned that, after having spent almost twenty years in preparation for turning Vader, to let him die would be a waste.
Though he had nearly left Vader to die back on Mustafar, Sidious held, perhaps, the merest sliver of affection for him that he had never held for Maul or Tyranus. The reason for this may lie in Vader's one-of-a-kind potential. To find another being even half as powerful could take many years, and even then it would probably never happen.
Back in the capital, at the Emperor Palpatine Surgical Reconstruction Center, Palpatine commanded that Vader be rebuilt using prosthetic replacements, a long and painful process that Palpatine made sure Vader would be kept conscious for, in order to make him stronger through pain. Upon being completely rebuilt and outfitted in a life-supporting suit of armor, Vader asked his master what had become of Padmé. How much of the story Palpatine knew is unknown, but he apparently believed Vader himself had killed his wife in his anger, which worked to his own advantage by breaking Anakin Skywalker's spirit once and for all; Anakin's transformation to Vader was now fully complete. Vader fell into a rage and destroyed the operating theater, and even attempted to reach out and kill Sidious. However, he proved unable to do so; his injuries had reduced his power in the Force as they had his physical capabilities, and would need to be similarly rebuilt. His knee-jerk reaction having failed to destroy Palpatine, Vader quickly ceased his efforts, realizing that Palpatine was all he had left; the only one who would accept him. Palpatine was pleased: one of the most powerful Sith Lords of all time was born in pain and suffering, and it was his apprentice.
Ever since the setback on Mustafar, Palpatine was disappointed to see his apprentice wither away into a broken shell of the man he once was. Palpatine had spent years engineering Anakin Skywalker's fall to the dark side, only to see his life's work all but destroyed because of Vader's carelessness.