Dooku was Qui-Gon's master, and therefore basically his father figure. Qui-Gon was the same for Obi-Wan. Dooku likely viewed Obi-Wan as something of a grandson.
Even before Obi-Wan discovered that Dooku had fallen to the dark side, he refused out of loyalty to the Republic and distaste for the Separatists' oppressive leadership. Unsurprisingly, this disappointed Dooku, who likely also sought to recruit Obi-Wan for his strength in the Force and skill in combat.
Like many of the other Sith, Count Dooku was incredibly proficient with the Force, even being able to win a fight against Yoda. Despite this, though, he still wasn't the best fighter with a lightsaber, and his Force skills were not nearly as powerful as Darth Vader's.
His best friend had been given a gift that could have allowed the Jedi to help countless people, but Yoda refused to act. As a Jedi, Dooku couldn't stand the thought that his best friend was suffering without a purpose, so he hated Yoda and the Jedi Order for that. In the end, though, Yoda was right.
Bottom line, Dooku never considered himself a Sith. And he wasn't; he was a man looking to change the galaxy in a way the Jedi were unwilling to try. And that is why he joined the Sith and became Darth Sidious' apprentice, Darth Tyrannus. When Dooku became Sidious's apprentice, he was already an elderly man.
1 Darth Sidious
There has been no Sith, as powerful, meticulous, nor as evil as the Emperor himself, Darth Sidious. As previously mentioned, Sidious trained in the Dark Side by Darth Plagueis before Sidious killed Plagueis in his sleep, making Sidious a Sith Master.
Truly, the most powerful Sith Lord was Darth Sidious, better known in his public persona of Chancellor (later Emperor) Palpatine. Through cunning and manipulation, Sidious killed his master to claim the mantle of Dark Lord of the Sith.
The count bested both Jedi in their duel, using the power of the dark side and taking advantage of young Skywalker's impetuous nature. But before he could land a killing blow, Master Yoda entered the fray. Not even Dooku's Sith-enhanced powers were enough for him to defeat Yoda.
Anakin regrets this decision, and Palpatine reasons with him saying that Dooku was too dangerous.
In legends, Dooku actually explains why he hates Anakin: He could feel Yoda's touch still lingering on the edges like a distant echo. Vividly his mind went back to their last meeting, on Geonosis: swords drawn at last, and finally equal.
With a potential Jedi Code-defying love affair with another Jedi, Dooku is more of a foil to his Clone Wars-era enemies, Anakin Skywalker and Obi-Wan Kenobi, with Dooku's lover, Jedi Master Jocasta Nu, possibly retaining feelings for Dooku well after he joined the ranks of the Lost Twenty.
Revenge of the Sith (2005)
Anakin gives in to his hatred of Dooku and uses his anger to overpower him, severing both of Dooku's hands and leaving him helpless.
Studying Jedi Archive records, Dooku based his new weapon design after the curved hilts that were standard during the heyday of Form II lightsaber combat. The curve allowed the hilt to fit better into his hand, allowing for superior finesse and precise blade control.
A former Jedi Master, Dooku had lost faith in the Republic and in the Jedi, believing them to be too tied to a corrupt political institution. He left the Jedi and fell under the sway of Darth Sidious, apprenticing to him in the hopes of bringing peace and order to the galaxy.
killed by an Imperial strike team, his dark side, like many Seth before him, refused to let go of life.
As impressive as Vader's battle tactics might be, if he and Revan make a stand with comparable armies, Revan is likely to be victorious. So, this point goes to Revan as well.
According to Star Wars Legends content, the first Sith was a former Jedi Master, Ajunta Pall, who became a so-called Dark Jedi, or “Fallen” Jedi. As the name implies, these Force-sensitives chose to practice the Dark Side, and rejected the Light Side of the Force.
The relationship between Sith Apprentice Count Dooku and Jedi Knight/General Anakin Skywalker is one of the main enmity relationships seen in Star Wars: The Clone Wars. Anakin has a personal vendetta against Dooku because he had dismembered Anakin's limb and cuased him to get a mechanical arm.
Thus, while Qui-Gon was less powerful than Yoda, Palpatine feared him more.
Dooku Wanted to Destroy the Sith and the Jedi with Obi-Wan
But Obi-Wan was resolute in his belief that the Jedi were dedicated to good deeds, with honorable members who were neither corrupt nor greedy.