Overall, Dooku was far more equipped to become a Sith Master than Maul was. Had he managed to overthrow Palpatine, Dooku would have been able to use his position, combat abilities, and dark side Force powers to take his place on the throne Palpatine had carved.
Anakin Skywalker was one of the strongest Jedi in the films and Darth Vader was one of the best Sith. It only makes sense that they both could have decimated Darth Maul if they faced him. At the peak of Anakin's power, he was able to take on Count Dooku and win, and went toe-to-toe with Obi-Wan on Mustafar.
The Separatists are able to weaken Darth Maul's Shadow Collective army and send him towards Talzin, but the Dathomir witch refuses to be baited and instead has Maul capture Count Dooku and General Grievous on Ord Mantell.
By the time of Episode 3; Anakin is in his prime, and already one of the Jedi Order's most powerful “masters” (although technically still a knight), just behind Obi-Wan, Windu, and Yoda. Maul wouldn't stand a chance.
Obi-Wan CONFIRMS Who is More Powerful - Maul or Dooku
Could Maul beat Sidious?
It's already been shown in the source material… more than once… that Darth Maul is not on Darth Sidious's level. Every time he dueled Sidious as his apprentice (in Legends) he got easily defeated. In the show Star Wars: The Clone Wars, Palpatine takes on Darth Maul and Savage Opress simultaneously.
The two were able to free Maul after he had been interrogated by the Sith Lord Count Dooku, and together the three rendezvoused with more Death Watch forces on the moon of Zanbar. Maul took command of his forces once again, and assured them that the war they had longed for was at hand.
Dooku despises Maul for being a threat to him, and for killing his beloved padawan Qui-Gon, and Maul hated Dooku for being his replacement. They also didn't regard each other as a true Sith: Dooku saw Maul as nothing more than a trained animal and Maul saw Dooku as a Sith pretender.
7 Why Rey Couldn't Win: Dooku's Skills Far Outshine Rey's
Rey was able to triumph over a lot of foes through sheer pluckiness and a good mixture of luck and sheer Force power. That won't help her against Dooku.
That notwithstanding, Master Windu was also one of the best. If the two spared as Jedi, Dooku would probably win the match because he was the better all-around duelist.
Considering his infamy, it's hard to deny that Darth Vader is the more powerful of the two, but his victory over Maul wouldn't come easily. As the Emperor's enforcer, Vader is terrifying.
The real reason for Obi-Wan's victory, though, may have been that he was the better fighter. While Darth Maul's moves were flashy, Obi-Wan eventually proved himself as one of the best duelists in the galaxy, and his fight with Maul was just the awakening of his skills.
Sidious revealed to Maul that he did not intend to kill his former apprentice, as he still had use for Maul; it was Sidious' hope that Maul would lead the Sith to Mother Talzin, Maul's mother and the leader of the Nightsisters, so she could be eliminated as a potential threat to the eventual Sith rule of the galaxy.
He fell under the influence of Supreme Chancellor Palpatine of Naboo, and left the Jedi Order. After learning that Palpatine was secretly the Sith Lord Darth Sidious, Dooku turned to the dark side and became a Dark Lord of the Sith himself, replacing Darth Maul as Sidious's second apprentice.
While Dooku was certainly evil -- and even had a Darth sobriquet, Tyranus, that he rarely used -- he was never quite a Sith, at least not in the true sense. Unlike those who espoused the Sith doctrine, Dooku wasn't motivated by hatred or fear, but by the same purpose that drove him as a Jedi.
Like his master, Darth Sidious, better known as Sheev Palpatine, Maul's main weakness was his overconfidence. In Luke Skywalker's confrontation with Palpatine during The Return of the Jedi, he tells the Emperor that his overconfidence is his weakness.
Yoda is extremely wary of the dark side, he knows that it clouds judgment. Maul is a prime example of this. Yoda would easily be able to outmaneuver Darth Maul and then outsmart him.
Maul seemingly gained the upper hand several times throughout their duel, yet he and Obi-Wan may not actually have been as evenly matched as viewers thought. It seemed like Obi-Wan managed to defeat Darth Maul against all odds, but the characters' timelines suggest Obi-Wan had the upper hand from the start.
As the Chosen One in his prime, it's quite possible that Anakin would have had a strong chance of defeating Palpatine aka Dark Sidious. Palpatine himself told Yoda before their Revenge of the Sith duel on Coruscant that Darth Vader would become more powerful than either of them as he continued to grow in the dark side.
