Qui Gon was having a hard time going up against Darth Maul and ultimately he was killed by Maul. The reason was that Qui Gon was old, he was over the hill, past his prime whereas Darth Maul was at his prime. That being the case, in the fight where Anakin goes up against Count Dooku the first time he loses and he loses an arm, in that same fight Obi Wan also loses. Now, Count Dooku is old, he is older than Qui Gon. As it is, Count Dooku was Qui Gon's teacher before he turned to evil, so he is significantly older than Qui Gon. If Qui Gon lost against Darth Maul because he was over the hill, than how is it that Count Dooku, who is older than Qui Gon and thus even more over the hill, able to beat both a budding Anakin and Obi Wan at his prime? It was only when Yoda came to the rescue that Anakin and Obi Wan were saved.
This is easy. It is addressed in the fiction, sort of. Qui Gon was a bit of a black sheep amongst the Jedi in a lot of ways. But he wasn't known as a terribly great swordsman. He was revered in other ways.
Age has a little to do with it but not very much. The Jedi do train in physical fitness according to the books but a lot of their swordplay is used with the assistance of the Force, which is why 800+ year old Yoda is still a bad mama jamma.
If I recall, Yoda was obviously revered as the best, followed by Dooku and Mace Windu, who weren't far from tying each other in ability.
Dooku was exceptionally good, better than the movies gave him credit for. His particular form is very graceful and more suited to dealing with one opponent, in melee. The fact that he could hold his own against two Jedi like Obi and Anakin is phenomenal.
Plus, like Bob said, Anakin was using Ataru, which is not very defensive. Wookieepedia quotes Yoda as saying that only true masters of Ataru can make it work defensively, which clearly he was the only true master you saw in the movies.
In their second encounter, Anakin was using a more powerful style than Ataru. I think he adapted Windu's style or something similar.
BTW, Darth Maul was probably as bad as they come. The books butter him up, but with how much he trained, he should have been able to eat anyone's lunch, maybe except for Yoda. It was through a psychologically traumatic event that Obi was able to kill him.
Otherwise, the movies would have been pointless.
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"He who knows not and knows not he knows not: He is a fool. Shun him. He who knows not and knows he knows not: He is simple. Teach him. He who knows and knows not he knows: He is asleep. Awaken him. He who knows and knows that he knows: He is wise. Follow him."
- Bruce Lee