Anakin Skywalker had lightsaber duels with Count Dooku several times in Star Wars: The Clone Wars and their battles improved Anakin’s character arc in the Star Wars live-action prequels. Anakin was arrogant in Star Wars: Episode II - Attack of the Clones, believing that he rivaled Yoda himself in his skills with a lightsaber. As a Padawan, Anakin was undoubtedly skilled and powerful, and this, combined with his lack of true defeats at the time, made him feel almost invincible. This changed when Count Dooku (aka Sith Lord Darth Tyranus) trounced Anakin on Geonosis, cutting off his arm and damaging his ego. Three years later in Star Wars: Episode III - Revenge of the Sith, a war-hardened and vengeful Anakin had his long-awaited rematch with Dooku, where he overpowered the Sith Lord and executed him, giving in to the dark side’s temptation.
In the original Star Wars timeline, the Expanded Universe (renamed Legends by Disney), Anakin didn’t have a genuine rematch with Dooku until Revenge of the Sith. In the 2002 Clone Wars video game, Anakin encounters Count Dooku during the Clone Wars on Raxus Prime one month into the war. They fight for only a few seconds before Anakin is rendered unconscious by the bounty hunter Cydon Prax, who stuns Anakin from behind with a blaster. Months later, as shown in the video game Star Wars: The New Droid Army, Anakin fights a doppelgänger of Dooku. Though a creation of the dark side, the doppelgänger isn’t as deadly as the real Dooku and is killed by Anakin. The Legends-era Clone Wars material preserves Anakin’s grudge with Dooku for the entirety of the three-year war, arguably improving his prequel trilogy arc by bringing him frustratingly close to the rematch he wants.
Anakin duels Count Dooku five times in the Star Wars Canon continuity of The Clone Wars. Four of the duels are inconclusive, with Dooku or Anakin retreating for various reasons. Anakin and Dooku’s duel on Naboo in season 4 ends with yet another victory for Dooku (albeit with assistance from his MagnaGuards). Although their repeated encounters contradict their dialogue in Revenge of the Sith, Anakin’s repeated inability to defeat Dooku further agitates his need for revenge. In a way, this is a different kind of improvement on his prequel trilogy story.
In Legends, Dooku isn’t the only dark side user Anakin fights during the Clone Wars. The Rattataki Sith acolyte Asajj Ventress is a reoccurring opponent for Anakin in 2003’s Star Wars: Clone Wars and the Legends-era Clone Wars comics. Anakin defeats Ventress in each of their encounters (though none are easy victories). This once again preserves Anakin’s grudge with Dooku, as it gives him the impression that a true Dark Lord of the Sith is more powerful than even the greatest Jedi, and that perhaps the only way to become more powerful than Dooku is to follow the path of the Sith as well.
Anakin fights Asajj Ventress in Canon as well, along with the Sith-trained Nightbrother Savage Oppress. Unlike in Legends, Anakin doesn’t always prevail against Dooku’s disciples, occasionally being overpowered by Ventress and proving unable to subdue Oppress in both of their encounters. Similar to his arc in Legends, Anakin’s inconsistent victories against dark side users in Star Wars: The Clone Wars give the impression that his adherence to the Force and the way of the Jedi is inadequate when compared to the dark side’s power and the Sith Order’s philosophies. Both the Canon and Legends versions of Clone Wars improve on Anakin’s prequel-era character development in different ways.
