Actually no. Mace Windu beat Sidious through the use of the Vaapad form (created by Windu himself). Vaapad acts as a sort of siphon of the Dark Side. If his opponents use the Dark Side, the form draws that Darkness into Mace Windu, which he uses to enhance his dueling and Force skills. Mace Windu was very close to falling to the Dark Side in his duel with Sidious.
Sidious is a master of the seven Lightsaber forms and could wield them with either hand, giving him the element of surprise in a duel. Seeing a duelist switch hands mid-duel can throw off many duelists. He was a very capable duelist, but he really specializes in Force power.
As great a duelist as Dooku and Qui-Gon are, they aren't on the same level as Sidious. And because they don't have Vaapad, they wouldn't be able to beat Sidious. Very few duelists can beat him. We have seen him beat Yoda and Luke in a duel. Granted Luke wasn't in his prime, but it is still an amazing feat.
This makes since, I guess I hadn't realized that Mace wasn't at his best when fight Dooku and Qui-gon 'cause he wasn't able to use Vaapad. This would explain a lot. Vaapad is a very complicated form that I think is worthy of a thread, hint, hint.