Most sources I've come across that reference post-Mustafar Anakin being 'weaker' typically have to do with the following:
a.) He can never conjure force lightning.
b.) The cybernetics of the suit make him more vulnerable to force lightning.
c.) The bulk of the suit hindered his overall agility.
The notion that Vader was "crippled by the lingering pain of his injuries" and a "shadow of his former self", however, is complete BS that has been retconned in canon.
We now know that the pain Vader experienced on a day-to-day basis actually served to strengthen him:
Without the neural connection to his armor, he was conscious of the stumps of his legs, the ruin of his arms, the perpetual pain in his flesh. He welcomed it. Pain fed his hate, and hate fed his strength. Once, as a Jedi, he had meditated to find peace. Now he meditated to sharpen the edges of his anger.-Lords of the Sith
Drawing on the Force, he activated the automated arm. It descended and the helmet and faceplate wrapped his head in metal and plasteel, the shell in which he existed. He welcomed the spikes of pain when the helmet's neural needles stabbed into the flesh of his skull and the base of his spine, unifying his body, mind, and armor to form an interconnected unit.When man and machine were one, he no longer felt the absence of his legs or arms, the pain of his flesh, but the hate remained, and the rage still burned. Those, he never relinquished, and he never felt more connected to the Force than when his fury burned.
With an effort of will, he commanded the onboard computer to link the primary respirator to the secondary, and to seal the helmet at the neck, encasing him fully. He was home.
-Lords of the Sith
Originally posted by xPRIMExIf you want direct quotes I can provide them but this is what Stover's novel says:
Proof?
Dooku started to regain the edge over Anakin with a simple taunt. Dooku became his playful sarcastic self again and Sidious could tell that he was going to beat Anakin.
Palpatine then intervened by telling Anakin to focus his anger, not to fear it, and unleash it on Dooku—to kill Dooku.
So as Anakin was unleashing hell on him, Dooku was taken aback by Sidious's intervention and his command to kill Dooku. It was at this moment he was learning of the treachery to come, asking himself "who's side was Sidious on anyway?".